Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1.

Question

w = 7j − 4i

Answer 1

unit vector in the same direction

= (4/sqr65)i + (7/sqr65)j

you get sqr65 from sqr(4^2 + 7^2 = sqr(16+49)

applying the Pythagorean Theorem

Answer 2

w = -4i + 7j

ll w ll = magnitude of w = √ [(-4)² + (7)²] = √65

u = unit vector in the direction of w = (1 / √65)(-4i + 7j) = (-4/√65)I + (7/√65)j

ll u ll = √ [(-4/√65)² + (7/√65)²] = √(65/65) = 1