Question

The resultant of A and B is perpendicular to Ā
What is the angle between A and B ?
(1) cos^-1 (a/b)
(2) cos^-1 (-a/b)
(3) sin^-1 (a/b)
(4)sin^-1 (-a/b)​

Answer 1

Answer:

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is. a) 30°

Answer 2

$Cos^{-1} (-\frac{A}{B} )$

Explanation:

Given that,

The resultant of A and B is ⊥ to Ā

So,

The angle between  Ā and the resultant vector(vector A + vector B) = 90°

Since the resultant vector is ⊥ to the actual vector.

∵ α = 90°

This suggests that,

Tan 90° = (B Sin θ)/( A + B Cos θ)

Since Tan 90° = ∞, in order to solve it, the denominator must be 0. So,

A + B Cos θ = 0

⇒ Cos θ = - (B/A)

∵ θ(angle between A and B) = $Cos^{-1} (-\frac{A}{B} )$

Thus, option 2 is the correct answer.

Learn more: Find the angle

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