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Chapter 10: Q 13 (page 848)

Describe the meaning of mathematical expression ${proj}_{u} v$ .

Short Answer

Expert verified

It represents the project of vector v onto u.

Step by step solution

Given information

A mathematical expression ${proj}_{u} v$

Describing the mathematical expression

The expression ${proj}_{u} v$ represents the projection of vector v onto u.

${proj}_{u} v = \frac{u . v}{{||u||}^{2}} u$

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Most popular questions from this chapter

Suppose that we know the reciprocal rule for limits: If $\lim_{x \to c} g (x) = M$ exists and is nonzero, then $\lim_{x \to c} \frac{1}{g (x)} = \frac{1}{M}$ This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

Find the norm of the vector. $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$

If the triple scalar product $u \cdot (v \times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

In Exercises 24-27, find ${comp}_{u} v, {proj}_{u} v$ and the component of v orthogonal tou.

$u = <3, - 1, 2>, v = <- 4, - 6, 3>$

Give an example of three nonzero vectors u, v and w in $ℝ^{3}$ such that $u \times v = u \times w$ but $v \neq w$ . What geometric relationship must the three vectors have for this to happen?

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Describe the meaning of mathematical expressionprojuv.

Short Answer

Step by step solution

Given information

Describing the mathematical expression

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Most popular questions from this chapter

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Describe the meaning of mathematical expression ${proj}_{u} v$ .