Question

How many unit vectors are there for which cosa = 1/2 and cosb =1/2, where a and b are angles made with X axis and Y-axis, respectively.

Answer 1

Explanation:

Since the vectors a+2b+ and 5a−4b are perpendicular so

(a+2b)⋅(5a−4b)=0

⇒5∣a∣

2

+6a⋅b−8∣b∣

2

=0

⇒6a⋅b=3(∣a∣=∣b∣=1)

⇒a⋅b=1/2⇒cosθ=1/2(∵∣a∣=∣b∣=1)

⇒θ=60

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