SATHEE: Motion in a Plane - Result Question 9

Motion in a Plane - Result Question 9

11. If $| \vec{A} \times \vec{B} | = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $| \vec{A} + \vec{B} |$ is

[2004]

(a) $(A^{2} + B^{2} + \sqrt{3} A B)^{1 / 2}$

(b) $(A^{2} + B^{2} + A B)^{1 / 2}$

(c) $(A^{2} + B^{2} + \frac{A B}{\sqrt{3}})^{1 / 2}$

(d) $A + B$

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Answer:

Correct Answer: 11. (b)

Solution:

(b) $| \vec{A} \times \vec{B} | = A B \sin θ$

$\vec{A} \cdot \vec{B} = A B \cos θ$

$| \vec{A} \times \vec{B} | = \sqrt{3} \vec{A} \cdot \vec{B} \Rightarrow A B \sin θ = \sqrt{} 3 A B \cos θ$

or, $\tan θ = \sqrt{3}, ∴ θ = 60^{\circ}$

$∴ | \vec{A} + \vec{B} | = \sqrt{A^{2} + B^{2} + 2 A B \cos 60^{\circ}}$

$- = \sqrt{A^{2} + B^{2} + A B}$

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Motion in a Plane - Result Question 9

11. If |A→×B→|=3A→⋅B→ then the value of |A→+B→| is

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11. If $| \vec{A} \times \vec{B} | = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $| \vec{A} + \vec{B} |$ is