# Recent questions tagged euclidean

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Verify that the Cauchy-Schwarz inequality holds. (a) $\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)$ (b) $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
Verify that the Cauchy-Schwarz inequality holds. (a) $\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)$ (b) $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$Verify that the Cauchy-Schwarz inequality holds. (a) $\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)$ (b) $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$ ...
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$Verify that the Cauchy&amp;ndash;Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$ ...
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$Verify that the Cauchy&amp;ndash;Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$ ...
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$Verify that the Cauchy&amp;ndash;Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$ ...
Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition.Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy 0 answers 7 views Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy $$\cos \ ... close 0 answers 101 views Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 /(i+1). Find the dot product of \mathbf{u} and \mathbf{v}.Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 ... close 1 answer 5 views If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}= ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonal 1 answer 2 views Show that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonalShow that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonal ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0},z_{0}\right)$and the line$a x+b y+c z+d=0$in$R^{3} ?$1 answer 5 views What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0},z_{0}\right)$and the line$a x+b y+c z+d=0$in$R^{3} ?$What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0},z_{0}\right)$and the line$a x+b y+c z+d=0$in$R^{3} ?$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that, In$R^{3}$the distance$D$between the point$P_{0}\left(x_{0}, y_{0}, z_{0}\right)$and the plane$a x+b y+c z+d=0$is 1 answer 8 views Prove that, In$R^{3}$the distance$D$between the point$P_{0}\left(x_{0}, y_{0}, z_{0}\right)$and the plane$a x+b y+c z+d=0$isProve that, In$R^{3}$the distance$D$between the point$P_{0}\left(x_{0}, y_{0}, z_{0}\right)$and the plane$a x+b y+c z+d=0$is $$D=\frac{\left| ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. 1 answer 6 views Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1.Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. ... close 1 answer 3 views The planes$$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$are parallel since their normals, (1,2,-2) and (2,4,-4), are parallel vectors. Find the distance between these planes.The planes$$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$are parallel since their normals, (1,2,-2) and (2,4,-4), are parallel vectors. Find the d ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that \mathbf{v}=(a, b) and \mathbf{w}=(-b, a) are orthogonal vectors. 0 answers 4 views Show that \mathbf{v}=(a, b) and \mathbf{w}=(-b, a) are orthogonal vectors.Show that \mathbf{v}=(a, b) and \mathbf{w}=(-b, a) are orthogonal vectors. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. 0 answers 3 views Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain.Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do? 0 answers 2 views A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do?A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do ... close 0 answers 5 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the lengths of the sides and the interior angles of the triangle in R^{4} whose vertices are$$ P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2) $$0 answers 5 views Find the lengths of the sides and the interior angles of the triangle in R^{4} whose vertices are$$ P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2) $$Find the lengths of the sides and the interior angles of the triangle in R^{4} whose vertices are$$ P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The angle between vectors$(1,3,-2)$and$(4,-2,-1)$is 0 answers 7 views The angle between vectors$(1,3,-2)$and$(4,-2,-1)$isThe angle between vectors$(1,3,-2)$and$(4,-2,-1)$is &nbsp; A) 0 B)$\dfrac{\pi}{3}$C)$\dfrac{\pi}{2}$D)$\pi$E) none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point$(1,1,1)$to the plane$ 2 x-10 y+11 z-4=0 $is equal to 0 answers 4 views The distance from the point$(1,1,1)$to the plane$ 2 x-10 y+11 z-4=0 $is equal toThe distance from the point$(1,1,1)$to the plane$ 2 x-10 y+11 z-4=0 $is equal to &nbsp; A)$\dfrac{1}{3}$B) 3 C)$\dfrac{1}{15}$D) 5 E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether planes$2 x+y+z-1=0,-x+3 y-2 z-3=0$and$3 x-y=-1$intersect. If yes, find the intersection. 0 answers 4 views Determine whether planes$2 x+y+z-1=0,-x+3 y-2 z-3=0$and$3 x-y=-1$intersect. If yes, find the intersection.Determine whether planes$2 x+y+z-1=0,-x+3 y-2 z-3=0$and$3 x-y=-1$intersect. If yes, find the intersection. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0}\right)$and the line$a x+b y+c=0$in$R^2$? 1 answer 4 views What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0}\right)$and the line$a x+b y+c=0$in$R^2$?What is the distance$D$between the point$P_{0}\left(x_{0}, y_{0}\right)$and the line$a x+b y+c=0$in$R^2$? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The angle between vectors$(2,6,-4)$and$(4,-2,-1)$is 0 answers 6 views The angle between vectors$(2,6,-4)$and$(4,-2,-1)$isThe angle between vectors$(2,6,-4)$and$(4,-2,-1)$is &nbsp; A. 0 B.$\dfrac{\pi}{3}$C.$\dfrac{\pi}{2}$D.$\pi$E. none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The angle between vectors$(1,3,-2)$and$(4,-2,-1)$is 0 answers 4 views The angle between vectors$(1,3,-2)$and$(4,-2,-1)$isThe angle between vectors$(1,3,-2)$and$(4,-2,-1)$is &nbsp; A) 0 B)$\frac{\pi}{3}$C)$\frac{\pi}{2}$D)$\pi$E) none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point$(-1,1,1)$to the plane 0 answers 5 views The distance from the point$(-1,1,1)$to the planeThe distance from the point$(-1,1,1)$to the plane $$2 x-10 y+11 z-4=0$$ is equal to &nbsp; A) 3 B)$\frac{1}{3}$C) 5 D)$\frac{1}{5}\$ E) no ...