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Which of the following vectors in $R^{6}$, if any, are parallel to $\mathbf{u}=(-2,1,0,3,5,1) ?$
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Which of the following vectors in $R^{6}$, if any, are parallel to $\mathbf{u}=(-2,1,0,3,5,1) ?$Which of the following vectors in $R^{6}$, if any, are parallel to $\mathbf{u}=(-2,1,0,3,5,1) ?$ (a) $(4,2,0,6,10,2)$ (b) $(4,-2,0,-6,-10,-2)$ (c) $(0 ...
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For what value(s) of $t$, if any, is the given vector parallel to $\mathbf{u}=(4,-1)$ ?
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For what value(s) of $t$, if any, is the given vector parallel to $\mathbf{u}=(4,-1)$ ?For what value(s) of $t$, if any, is the given vector parallel to $\mathbf{u}=(4,-1)$ ? (a) $(8 t,-2)$ (b) $(8 t, 2 t)$ (c) $\left(1, t^{2}\right)$ ...
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Let $\mathbf{u}=(1,-1,3,5)$ and $\mathbf{v}=(2,1,0,-3)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(1,-4,9,18)$.
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Let $\mathbf{u}=(2,1,0,1,-1)$ and $\mathbf{v}=(-2,3,1,0,2)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(-8,8,3,-1,7)$
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Find scalars $c_{1}, c_{2}$, and $c_{3}$ for which the equation is satisfied.
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Find scalars $c_{1}, c_{2}$, and $c_{3}$ for which the equation is satisfied. Find scalars $c_{1}, c_{2}$, and $c_{3}$ for which the equation is satisfied. $c_{1}(1,-1,0)+c_{2}(3,2,1)+c_{3}(0,1,4)=(-1,1,19)$ $c_{1}(- ...
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Show that there do not exist scalars $c_{1}, c_{2}$, and $c_{3}$ such that $$ c_{1}(-2,9,6)+c_{2}(-3,2,1)+c_{3}(1,7,5)=(0,5,4) $$
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Show that there do not exist scalars $c_{1}, c_{2}$, and $c_{3}$ such that $c_{1}(1,0,1,0)+c_{2}(1,0,-2,1)+c_{3}(2,0,1,2)=(1,-2,2,3)$
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Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$.
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Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$.Let $P$ be the point $(2,3,-2)$ and $Q$ the point $(7,-4,1)$. (a) Find the midpoint of the line segment connecting the points $P$ and $Q$. (b) Find th ...
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In relation to the points $P_{1}$ and $P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin?
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Let $P$ be the point $(1,3,7)$. If the point $(4,0,-6)$ is the midpoint of the line segment connecting $P$ and $Q$, what is $Q$ ?
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If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.
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True/False: Two equivalent vectors must have the same initial point
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True/False: Two equivalent vectors must have the same initial pointTrue/False: Two equivalent vectors must have the same initial point ...
by MathsGee Platinum
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asked in Mathematics 19 hours ago
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True/False: The vectors $(a, b)$ and $(a, b, 0)$ are equivalent.
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True/False: The vectors $(a, b)$ and $(a, b, 0)$ are equivalent.True/False: The vectors $(a, b)$ and $(a, b, 0)$ are equivalent. ...
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True/False: If $k$ is a scalar and $\mathbf{v}$ is a vector, then $\mathbf{v}$ and $k \mathbf{v}$ are parallel if and only if $k \geq 0$.
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True/False: The vectors $\mathbf{v}+(\mathbf{u}+\mathbf{w})$ and $(\mathbf{w}+\mathbf{v})+\mathbf{u}$ are the same.
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True/False: If $\mathbf{u}+\mathbf{v}=\mathbf{u}+\mathbf{w}$, then $\mathbf{v}=\mathbf{w}$
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True/False: If $\mathbf{u}+\mathbf{v}=\mathbf{u}+\mathbf{w}$, then $\mathbf{v}=\mathbf{w}$True/False: If $\mathbf{u}+\mathbf{v}=\mathbf{u}+\mathbf{w}$, then $\mathbf{v}=\mathbf{w}$ ...
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asked in Mathematics 19 hours ago
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True/False: If $(a, b, c)+(x, y, z)=(x, y, z)$, then $(a, b, c)$ must be the zero vector.
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True/False: If $(a, b, c)+(x, y, z)=(x, y, z)$, then $(a, b, c)$ must be the zero vector.True/False: If $(a, b, c)+(x, y, z)=(x, y, z)$, then $(a, b, c)$ must be the zero vector. ...
by MathsGee Platinum
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asked in Mathematics 19 hours ago
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True/False: If $k$ and $m$ are scalars and $\mathbf{u}$ and $\mathbf{v}$ are vectors, then $$ (k+m)(\mathbf{u}+\mathbf{v})=k \mathbf{u}+m \mathbf{v} $$
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True/False: If the vectors $\mathbf{v}$ and $\mathbf{w}$ are given, then the vector equation
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True/False: If the vectors $\mathbf{v}$ and $\mathbf{w}$ are given, then the vector equationIf the vectors $\mathbf{v}$ and $\mathbf{w}$ are given, then the vector equation $$ 3(2 \mathbf{v}-\mathbf{x})=5 \mathbf{x}-4 \mathbf{w}+\mathbf{v} $$ ...
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What is a norm of a vector?
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What is a norm of a vector?What is a norm of a vector? ...
by MathsGee Platinum
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How is the norm of a vector related to the Theorem of Pythagoras?
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How is the norm of a vector related to the Theorem of Pythagoras?How is the norm of a vector related to the Theorem of Pythagoras? ...
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What is the norm of the vector $\mathbf{v}=(-3,2,1)$ in $R^{3}$?
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What is the norm of the vector $\mathbf{v}=(-3,2,1)$ in $R^{3}$?What is the norm of the vector $\mathbf{v}=(-3,2,1)$ in $R^{3}$? ...
by MathsGee Platinum
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asked in Mathematics 19 hours ago
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What is the norm of the vector $\mathbf{v}=(2,-1,3,-5)$ in $R^{4}$?
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What is the norm of the vector $\mathbf{v}=(2,-1,3,-5)$ in $R^{4}$?What is the norm of the vector $\mathbf{v}=(2,-1,3,-5)$ in $R^{4}$? ...
by MathsGee Platinum
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asked in Mathematics 19 hours ago
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If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|\mathbf{v}\|=0$ if and only if $\mathbf{v}=\mathbf{0}$
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