Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by $p r o j_{u} v = \frac{u . v}{| |u| |}, w h e r e u \neq 0 .$

Question

Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by $p r o j_{u} v = \frac{u . v}{| |u| |}, w h e r e u \neq 0 .$

Accepted Answer

$D o t p r o d u c t : u . v = |u| |v| \cos θ, p r o j_{u} v = |v| \cos θ, S o l v i n g a b o v e t w o e q u a t i o n s w e g e t, p r o j_{u} v = \frac{u . v}{||u||} .$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by $p r o j_{u} v = \frac{u . v}{| |u| |}, w h e r e u \neq 0 .$

Step by Step Solution

Step 1. Given Information.

Step 2. Dot product.

Step 3. Proof

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by projuv = u.v|u|, where u≠0.

Step by Step Solution

Step 1. Given Information.

Step 2. Dot product.

Step 3. Proof

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Calculus

Pure Maths

Projecting one vector onto another: Show that the formula for the projection of a vector v onto a nonzero vector u is given by $p r o j_{u} v = \frac{u . v}{| |u| |}, w h e r e u \neq 0 .$