Q 29.

Question

In Exercises 28-31, find ${proj}_{u} v and {proj}_{v} u$ .

$u = <3, - 4>, v = <16, 12>$

Step-by-Step Solution

Verified

Answer

The values are ${proj}_{u} v = 0 and {proj}_{v} u = 0$ .

1Step 1. Given information.

The given vectors are:

$u = <3, - 4> and v = <16, 12>$

2Step 2. Find the vector projection of v onto u .

${proj}_{u} v = \frac{u \cdot v}{{||u||}^{2}} u u = <3, - 4> and v = <16, 12> u \cdot v = 3 (16) + (- 4) 12 = 48 - 48 = 0 ||u|| = \sqrt{3^{2} + {(- 4)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

Then,

${proj}_{u} v = \frac{u \cdot v}{{||u||}^{2}} u = \frac{0}{{(5)}^{2}} <3, - 4> = 0$

Therefore, ${proj}_{u} v = 0$ .

3Step 3. Find the vector projection of u onto v.

${proj}_{v} u = \frac{u \cdot v}{{||v||}^{2}} v u = <3, - 4> and v = <16, 12> ||v|| = \sqrt{{(16)}^{2} + {(12)}^{2}} = \sqrt{256 + 144} = \sqrt{400} = 20 {proj}_{v} u = \frac{u \cdot v}{{||v||}^{2}} v = \frac{0}{{(20)}^{2}} <16, 12> = 0$

Therefore, ${proj}_{v} u = 0$ .

Q 28.

Q 30.

Other exercises in this chapter

Q 27.

In Exercises 24-27, find compuv , projuv and the component of v orthogonal to u. u=3,1,-2, v=-6,-2,

View solution

Q 28.

In Exercises 28-31, find projuv and projvu.u=1,4, v=2,-3

View solution

Q 30.

In Exercises 28-31, find projuv and projvu.u=3,0,1, v=2,2,-5

View solution

Q 31.

In Exercises 28-31, find projuv and projvu.u=1,-5,-1, v=0,1,0

View solution