Resolve the following vectors into components:

(a) The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

v = _ i + _ j

(b) The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis.

v = _ i + _ j + _ k

Vectorv resolved into components is v = (3√2/2)i + (3√2/2)jVectorw resolved into components is w = 0i + (1/2)j + (√3/2)k## a. How to resolve vector v into components?

vectorin 2 dimension is given by r = xi + yjvectorv in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis, we have that,Vectorv resolved into components is v = (3√2/2)i + (3√2/2)j## b. How to resolve vector w into components?

vectorin 3 dimension is given by r = xi + yj + zkvectorw in 3-space of length 1 lying in the yz-plane pointing upwards at an angle of 2π/3 measured from the positive x-axis, we have that,Vectorw resolved into components is w = 0i + (1/2)j + (√3/2)kvectorshere: