The magnitude of the resultant of two vectors of magnitudes 3 units and 4 units in 5 units. What is the angle between 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 R of two vectors A and B inclined at an angle $θ$ is given by
$R^{2} = A^{2} + B^{2} + 2 A B cos θ$
$cos θ = \frac{R^{2} - A^{2} - B^{2}}{2 A B} = \frac{(5)^{2} - (3)^{2} - (4)^{2}}{2 \times 3 \times 4} = 0$
$∴$ $θ = \frac{π}{2} .$
Hence the correct choice is (b)

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

The correct option is B π2The 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 cosθ=R2−A2−B22AB=(5)2−(3)2−(4)22×3×4=0 ∴ θ=π2. Hence the correct choice is (b)