The angle between two vectors A and B is - Vector R is the resultant of the two vectors- If R makes an angle -2 with A- then

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Vector Addition

The angle bet...

Question

The angle between two vectors A and B is $θ$ . Vector R is the resultant of the two vectors. If R makes an angle $\frac{θ}{2}$ with A, then

A = 2 B

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A = \frac{B}{2}

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A = B

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A B = 1

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Solution

The correct option is B $A = B$
The angle $α$ which the resultant R makes with A is given by
$t a n α = \frac{B s i n θ}{A + B c o s θ}$
or $\frac{s i n (θ / 2)}{c o s (θ / 2)} = \frac{2 B s i n (θ / 2) c o s (θ / 2)}{A + B c o s θ}$
which gives $A + B c o s θ = 2 B c o s^{2} (\frac{θ}{2})$
or $A + B [2 c o s^{2} (\frac{θ}{2}) - 1] = 2 B c o s^{2} (\frac{θ}{2})$
$A = B$

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