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If $\left | A \right |=2$ and $\left | B \right |=4$ then match the relations in column I with the angle $\theta$ between A and B in column II.

    Column I                          Column II

(a) $\left | A\times B \right |=0$       (i) $\theta =30^{o}$

(b) $\left | A\times B \right |=8$          (ii) $\theta =45^{o}$

(c) $\left | A\times B \right |=4$          (iii) $\theta =90^{o}$

(d) $\left | A\times B \right |=4\sqrt{2}$     (iv) $\theta =0^{o}$

Answers (1)

Given : $\left | \vec{A} \right |=2$ and $\left | \vec{B} \right |=4$

a) Matches with (iv)

$\left | \vec{A}\times \vec{B} \right |=0$

$\left | \vec{A} \right |\left | \vec{B} \right |\sin \theta =0$

$2\times4\; \sin \theta =0$

$\sin \theta =\sin 0$

$\theta =0$

b) matches with (iii)

$\left | \vec{A}\times \vec{B} \right |=8$

$\left | \vec{A} \right |\left | \vec{B} \right |\sin \theta =8$

$2\times4\; \sin \theta =8$

$\sin \theta =1$

$\theta =90$

c) matches with (i)

$\left | \vec{A}\times \vec{B} \right |=4$

$\left | \vec{A} \right |\left | \vec{B} \right |\sin \theta =4$

$2\times4\; \sin \theta =4$

$\sin \theta =\frac{1}{2}$

$\theta =30$

d) matches with (ii)

$\left | \vec{A}\times \vec{B} \right |=4\sqrt{2}$

$\left | \vec{A} \right |\left | \vec{B} \right |\sin \theta =4\sqrt{2}$

$2\times4\; \sin \theta =4\sqrt{2}$

$\sin \theta =\frac{1}{\sqrt{2}}$

$\theta =45$

Posted by

infoexpert23

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