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Verify that the Cauchy-Schwarz inequality holds. (a) \(\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)\) (b) \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)\)

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Verify that the Cauchy–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 $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
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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
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Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal
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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
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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
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Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
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Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.
0 answers 4 views
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Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
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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?

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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   A) 0 B) $\dfrac{\pi}{3}$ C) $\dfrac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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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   A) $\dfrac{1}{3}$ B) 3 C) $\dfrac{1}{15}$ D) 5 E) no ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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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.
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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
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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   A. 0 B. $\dfrac{\pi}{3}$ C. $\dfrac{\pi}{2}$ D. $\pi$ E. none of the above ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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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   A) 0 B) $\frac{\pi}{3}$ C) $\frac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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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   A) 3 B) $\frac{1}{3}$ C) 5 D) $\frac{1}{5}$ E) no ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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