Question

For the vectors Bold uequalsleft angle negative 8 comma 0 comma 1 right angleand Bold vequalsleft angle 1 comma 3 comma negative 3 right angle​,calculate proj Subscript Bold v Baseline Bold uand sca l Subscript Bold v Baseline Bold u.

Answer 1

Answer:

Step-by-step explanation:

Given that there are two vectors U = (-8,0,1)

V = (1,3,-3)

To find projection of u on V and also projection of V on U

First let us find the dot product U and V

U.V = $-8(1)+0(3)+1(-3)\\= -11$

Projection of U on V =$\frac{U.V}{|V|} \\=\frac{-11}{\sqrt{1+9+9} } \\=\frac{-11}{\sqrt{19} }$

Similarly projection of V on U

=$\frac{U.V}{|U|} \\=\frac{-11}{\sqrt{64+0+1} } \\=\frac{-11}{\sqrt{65} }$