Which of the following relations is true for two unit vectors A and B making an angle θ to each other? (a) |A + B| = |A - B| tan (θ)/(2) (b) |A - B| = |A + B| tan (θ)/(2) (c) |A + B| = |A - B| cos (θ)/(2) (d) |A - B| = |A + B| cos (θ)/(2)

Answer: (b). For unit vectors: |A + B| = 2cos (θ)/(2), |A - B| = 2sin (θ)/(2). Dividing: (|A - B|)/(|A + B|) = tan (θ)/(2) So the answer is (b) |A - B| = |A + B|tan (θ)/(2).

Which of the following relations is true for two unit vectors A and B… | JEE Main 2022 (25 Jun, Shift 1)

Q16JEE Main 2022 · 25 JUN · SHIFT 1Medium

Addition & Subtraction of Vectors

Which of the following relations is true for two unit vectors $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each other?

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Answer: (b)

For unit vectors: $|\hat{A} + \hat{B}| = 2\cos\frac{\theta}{2}$ , $|\hat{A} - \hat{B}| = 2\sin\frac{\theta}{2}$ .
Dividing: $\frac{|\hat{A} - \hat{B}|}{|\hat{A} + \hat{B}|} = \tan\frac{\theta}{2}$
So the answer is (b) $|\hat{A} - \hat{B}| = |\hat{A} + \hat{B}|\tan\frac{\theta}{2}$ .

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