Given A - B - C and the magnitudes of vectors A - B and C are respectively 12-5 and 13 units- The angle between A and B isA- -B- zeroC- -2D- -4

The correct option is C π/2 If the angle between A and B is θ, the magnitude of the resultant is given by C^2=A^2+B^2+2AB cos θ ⇒ (13)^2=(12)^2+(5)^2+2× 12× 5× ...

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Byju's Answer

Standard XII

Physics

Vector Addition

Given A + B =...

Question

Given $\to A + \to B = \to C$ and the magnitudes of vectors $\to A$ , $\to B$ and $\to C$ are respectively 12, 5 and 13 units. The angle between $\to A$ and $\to B$ is

zero

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$π$

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$\frac{π}{2}$

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$\frac{π}{4}$

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Solution

The correct option is C
$\frac{π}{2}$

If the angle between $\to A$ and $\to B$ is $θ$ , the magnitude of the resultant is given by
$C^{2} = A^{2} + B^{2} + 2 A B c o s θ$
$\Rightarrow (13)^{2} = (12)^{2} + (5)^{2} + 2 \times 12 \times 5 \times c o s θ$
$\Rightarrow c o s θ = 0$
$\Rightarrow θ = \frac{π}{2}$ .
Hence, the correct choice is (c).

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