Question

When vectors b+a= 5i-j & vectors b-a=i-7j, what is the magnitude and direction of vector a

Answer 1

Eliminate b by combining b + a and b - a, and solve for a :

(b + a) - (b - a) = (5i - j) - (i - 7j)

2a = 4i + 6j

a = 2i + 3j

Now compute the magnitude and direction.

mag: ||a|| = √(2² + 3²) = √13

dir: tan(θ) = 3/2 ⇒ θ = arctan(3/2) ≈ 56.3°