Question

1. Let u (1.-3,2), v= (-1.4.2). Then find b) a unit vector in the same direction of 4v.

Answer 1

4v points in the same direction as v, so all you need to do is normalize v.

Simply multiply it by the reciprocal of its magnitude:

`v = (-1, 4, 2) \implies \|v\| = √((-1)^2 + 4^2 + 2^2) = √(21)`

`\implies (v)/(\|v\|) = ((-1,4,2))/(√(21)) = \left(-\frac1{√(21)}, \frac4{√(21)}, \frac2{√(21)}\right)`