Question

Q7 Q7.) Find the unit vector in the same direction as v.

Answer 1

Use Pythagorean theorem:

9i-j = sqrt (9^2 - 1^2) = sqrt(81-1) = sqrt80

now divide both terms in V by that:

u = 9/sqrt(80)i - 1/sqrt(80)j

see attached picture: 

Answer 2

|v| = sqrt(9^2+(-1)^2)=sqrt(82)

u = v/|v| = 9/sqrt(82) i - 1/sqrt(82) j