Evaluate the expression. r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1> v ⋅ w

Solution:

Given: Two vectors v and w.v and w are of the form <\(u_1\),\(u_2\),\(u_3\)> and <\(v_1\),\(v_2\),\(v_3\)>

To find the dot product of the two vectors, we sum the products of the two sequences of numbers.

u.v= \(u_1 v_1\)+\(u_2 v_2\)+\(u_3 v_3\)

Given, v = <3, 3, -8> and w = <9, -6, -1>

The dot product 

v . w = 3 × 9 + 3 × (-6) + (-8) × (-1)

v . w = 27 - 18 + 8

= 35 - 18

v . w = 17

Evaluate the expression. r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1> v ⋅ w

Summary:

The value of the expression. r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1> v . w is 17.