(-4,7)+(4,-4)=?

Regina Ewing
2022-05-07
Answered

(-4,7)+(4,-4)=?

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Raiden Williamson

Answered 2022-05-08
Author has **14** answers

Simplify the following:

$(-4,7)+(4,-4)$

Add the corresponding components of the vectors $(-4,7)$ and $(4,-4)$.

$(-4,7)+(4,-4)=(-4+4,7-4):$

$(-4+4,7-4)$

Look for the difference of two identical terms.

$-4+4=0:$

$(0,7-4)$

Subtract $4$ from $7$.

$7-4=3:$

Answer:

$(0,3)$

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Find the scalar and vector projections of b onto a.

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

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

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

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

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

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

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

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a)

b)

c)

d)

e)

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Projection of u onto v and v onto u

Given the vector$u=<-2,6,4>$ and a vector v such that the vector projection of u onto v is $<2,4,4>$ , and the vector projection of v onto u is $<-8,24,16>$ . What is the vector v?

Let$\overrightarrow{v}=<a,b,c>$

Projection of$\overrightarrow{v}\text{}on\to \text{}\overrightarrow{u}$ is given by:

$pro{j}_{u}v=\frac{\overrightarrow{u}.\overrightarrow{v}}{{\left|u\right|}^{2}}\overrightarrow{u}=\frac{\overrightarrow{u}.\overrightarrow{v}}{{(-2)}^{2}+{6}^{2}+{4}^{2}}<-2,6,4>$

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$\Rightarrow 4<-2,6,4\ge \frac{\overrightarrow{u}.\overrightarrow{v}}{4+36+16}<-2,6,4>$

$\Rightarrow <-2,6,4\ge \frac{\overrightarrow{u}.\overrightarrow{v}}{224}<-2,6,4>$

On comparing$\frac{\overrightarrow{u}.\overrightarrow{v}}{224}=1$

$\Rightarrow \overrightarrow{u}.\overrightarrow{v}=224$

$pro{j}_{v}u=\frac{\overrightarrow{u}.\overrightarrow{v}}{{\left|v\right|}^{2}}\overrightarrow{v}=\frac{224}{{\left|v\right|}^{2}}<a,b,c>$

$\Rightarrow <2,4,4\ge \frac{224}{{\left|v\right|}^{2}}<a,b,c>$

Dividing both sides by 2 we get:

$\Rightarrow <1,2,2\ge \frac{112}{{\left|v\right|}^{2}}<a,b,c>$

Given the vector

Let

Projection of

On comparing

Dividing both sides by 2 we get:

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