The magnitude of the resultant of two vectors of magnitude 3 units and 4 units in 5 units. What is the angle between the two vectors?

$\frac{π}{4}$

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$\frac{π}{2}$

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$\frac{3 π}{4}$

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$π$

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Solution

The correct option is B
$\frac{π}{2}$

The magnitude R of the resultant vector $\to R$ of two vectors $\to A$ and $\to B$ inclined at an angle $θ$ is given by $R^{2} = A^{2} + B^{2} + 2 A B c o s θ$
Here, $R^{2} = A^{2} + B^{2}$ , i.e., $5^{2} = 3^{2} + 4^{2}$
$\Rightarrow c o s θ = 0$
$∴ θ = \frac{π}{2}$
Hence, the correct choice is (b).

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The magnitude of the resultant of two vectors of magnitude 3 units and 4 units in 5 units. What is the angle between the two vectors?

The correct option is B π2 The magnitude R of the resultant vector →R of two vectors →A and →B inclined at an angle θ is given by R2=A2+B2+2ABcosθ Here, R2=A2+B2, i.e., 52=32+42 ⇒cos θ=0 ∴θ=π2 Hence, the correct choice is (b).