Why can ${v}_{x},{v}_{y}$ in $\mathbf{v}=(z,z,z)$ contain the z variable?

Matilda Fox
2022-07-23
Answered

Why can ${v}_{x},{v}_{y}$ in $\mathbf{v}=(z,z,z)$ contain the z variable?

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asked 2021-05-29

Which of the following expressions are meaningful? Which are meaningless? Explain.

a)$(a\cdot b)\cdot c$

$(a\cdot b)\cdot c$ has ? because it is the dot product of ?.

b)$(a\cdot b)c$

$(a\cdot b)c$ has ? because it is a scalar multiple of ?.

c)$|a|(b\cdot c)$

$|a|(b\cdot c)$ has ? because it is the product of ?.

d)$a\cdot (b+c)$

$a\cdot (b+c)$ has ? because it is the dot product of ?.

e)$a\cdot b+c$

$a\cdot b+c$ has ? because it is the sum of ?.

f)$|a|\cdot (b+c)$

$|a|\cdot (b+c)$ has ? because it is the dot product of ?.

a)

b)

c)

d)

e)

f)

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Find a vector equation and parametric equations for the line segment that joins P to Q.

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

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Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in $M}_{2\times 4$ with the property that FA = 0 (the zero matrix in ${M}_{3\times 4})$ . Determine if H is a subspace of $M}_{2\times 4$

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Find the scalar and vector projections of b onto a.

$a=(4,7,-4),b=(3,-1,1)$

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Determine whether the vectors ${\upsilon}_{1}=(-1,2,-3),{\upsilon}_{2}=(3,2,1),{\upsilon}_{3}=(5,6,-1)$ are linearly dependent or independent in ${\mathbb{R}}^{3}.$

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Find the scalar and the vector projections of vector b onto the direction of vector a, where a = [0, -2, -16] and b = [12, -16, -18].

asked 2022-08-25

1.Given a circle C with center A and radius r.

2.Given a line D with a vector u passing through point ${P}_{0}$.

3.Knowing that P is on D only if $P={P}_{0}+tu$

4.Knowing that P is on C if $\Vert {P-A}^{2}\Vert ={r}^{2}$

Prove that point P is on C and D if there exists a real number t where

$[\Vert u{\Vert}^{2}]{t}^{2}+[2({P}_{0}-A)\cdot u]t+[\Vert {{P}_{0}-A}^{2}\Vert -{r}^{2}]=0.$

What properties should I be using in order to solve this?

2.Given a line D with a vector u passing through point ${P}_{0}$.

3.Knowing that P is on D only if $P={P}_{0}+tu$

4.Knowing that P is on C if $\Vert {P-A}^{2}\Vert ={r}^{2}$

Prove that point P is on C and D if there exists a real number t where

$[\Vert u{\Vert}^{2}]{t}^{2}+[2({P}_{0}-A)\cdot u]t+[\Vert {{P}_{0}-A}^{2}\Vert -{r}^{2}]=0.$

What properties should I be using in order to solve this?