Use the dot product to find the magnitude of u.u = −26i Find the projection of u onto v.u = 4, 4 v = 7, 1 projvu = Write u as the sum of two orthogonal vectors, one of which is projvu.u = projvu +

The magnitude of u is 26. The vectors are given as: u=4i^+4j^v=7i^+j^ projvu=u·v|v|2·v…

Answered: Use the dot product to find the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section: Chapter Questions

Problem 21T

See similar textbooks

Related questions

Question

Use the dot product to find the magnitude of u.

u = −26i

Find the projection of u onto v.

4, 4

7, 1

proj_vu =

Write u as the sum of two orthogonal vectors, one of which is proj_vu.
u = proj_vu +

Expert Solution

Step 1

The magnitude of u is 26.

The vectors are given as:

$u = 4 \hat{i} + 4 \hat{j} v = 7 \hat{i} + \hat{j}$

$p r o j_{v} u = (\frac{u \cdot v}{| v |^{2}}) \cdot v p r o j_{v} u = (\frac{(4 \hat{i} + 4 \hat{j}) \cdot (7 \hat{i} + \hat{j})}{| (7 \hat{i} + \hat{j}) |^{2}}) \cdot (7 \hat{i} + \hat{j}) p r o j_{v} u = (\frac{28 + 4}{| 49 + 1}) \cdot (7 \hat{i} + \hat{j}) p r o j_{v} u = (\frac{32}{50}) \cdot (7 \hat{i} + \hat{j}) p r o j_{v} u = (\frac{16}{25}) (7 \hat{i} + \hat{j}) p r o j_{v} u = (\frac{112}{25} \hat{i} + \frac{16}{25} \hat{j})$

Step by step

Solved in 2 steps

Knowledge Booster

$Projection$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions