If A-B-C- and the magnitude of A- B- and C- are 5-4 and 3 units- respectively- then the angle between A- and C- is-

The correct option is C cos^ 1(3/5) Magnitude of A =AC=5, B =AB=4 & C =BC=3 #160; #160; #160;which forms a #160;Pythagoras triple ...

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Standard XII

Physics

Vector Addition

If A⃗=B⃗+C⃗...

Question

If $\to A = \to B + \to C$ and the magnitude of $\to A, \to B$ and $\to C$ are $5, 4$ and $3$ units, respectively, then the angle between $\to A$ and $\to C$ is:

\frac{π}{2}

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{sin}^{- 1} (3 / 4)

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{cos}^{- 1} (3 / 5)

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{cos}^{- 1} (4 / 5)

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Solution

The correct option is C ${cos}^{- 1} (3 / 5)$
Magnitude of $\to A = A C = 5, \to B = A B = 4 & \to C = B C = 3$
which forms a Pythagoras triplet
Let $θ$ be angle between $\to A & \to C$
$cos θ = \frac{3}{5}$ so, $θ = {cos}^{- 1} \frac{3}{5}$

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