Question

For what value of λ are the vectors vector a=2i+λj+k and vector b=i-2j+3k perpendicular to each other?​

Answer 1

If two vectors are perpendicular, their dot product is 0.

a = 2i+λj+k
b = i-2j+3k

a.b = 0

(2i+λj+k).(i-2j+3k) = 0

2 - 2λ + 3 = 0

2λ = 5

λ = 5/2