Gregory Jones
2021-12-16
Answered

Derivative of cross-product of two vectors $\frac{d}{dt}[\overrightarrow{u\left(t\right)}\times \overrightarrow{v\left(t\right)}]$ , is it possible to find the cross-product of the two vectors first before differentiating?

You can still ask an expert for help

asked 2021-05-17

Find the scalar and vector projections of b onto a.

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

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)

asked 2021-02-11

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 $M}_{2\times 4$

asked 2021-05-29

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)

asked 2022-08-21

The law of cosine is

$\Vert b-a{\Vert}^{2}=\Vert b{\Vert}^{2}+\Vert a{\Vert}^{2}-2\Vert b\Vert \Vert a\Vert \mathrm{cos}\theta $

Is there a way to prove this when vectors a,b have more than 3 components?

For 3 or less components one can prove it using geometry but what about higher dimensions?

$\Vert b-a{\Vert}^{2}=\Vert b{\Vert}^{2}+\Vert a{\Vert}^{2}-2\Vert b\Vert \Vert a\Vert \mathrm{cos}\theta $

Is there a way to prove this when vectors a,b have more than 3 components?

For 3 or less components one can prove it using geometry but what about higher dimensions?

asked 2021-06-04

Vectors

a)

b)

c)

asked 2021-08-20

Find the scalar and vector projections of b onto a.

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