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Chapter 10: Q 12 (page 801)

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Expert verified

The required vector is: $<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}>$

Step by step solution

Given information

Given a vector $<a, b, c>$

Finding the vector

The vector is in opposite direction so negative sign has to be applied and half means multiplying the vector with scalar $\frac{1}{2}$ .

The required vector is:

$<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}> .$

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Most popular questions from this chapter

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <1, 2>, v = <3, 5>$

Find a vector in the direction opposite to $<- 1, - 4, - 6>$ andwith magnitude 7.

If u and v are nonzero vectors in $ℝ^{3}$ , what is the geometric relationship between $u, v$ and $u \times v$ ?

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

role="math" localid="1649434688557" $v \times w and w \times v$

Find $\vec{P Q}$

$P = (- 1, 5, 4), Q = (- 1, 6, 4)$

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Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Find a vector parallel to a,b,cbut half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.