Given that C- A - B- The magnitude of A - B and C are 12-5 and 13 units respectively- The angle between A and B is A- 0-B- - C- -2D- -4

The correct option is C π/2If C = A + B, then magnitude of C and A + B are same nbsp; |C|=|A + B| |C| = √(A^2 + B^2 + 2AB cosθ) 13 = √(12^2 + 5^2 + 2 × 12 × ...

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Byju's Answer

Standard XII

Physics

Vector Addition

Given that C⃗...

Question

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

0^{\circ}

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\frac{π}{4}

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\frac{π}{2}

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π

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Solution

The correct option is C $\frac{π}{2}$
If $\to C = \to A + \to B$ , then magnitude of $\to C$ and $\to A + \to B$ are same
$| \to C | = | \to A + \to B |$
$| \to C | = \sqrt{A^{2} + B^{2} + 2 A B cos θ}$ $13 = \sqrt{12^{2} + 5^{2} + 2 \times 12 \times 5 cos θ}$
$\Rightarrow 169 = 144 + 25 + 2 \times 12 \times 5 cos θ$ $cos θ = 0 \Rightarrow θ = \frac{π}{2}$

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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