<p><strong>Let <math><mrow><mover accent="true"><mi>a</mi><mo>→</mo></mover><mo>=</mo><mn>3</mn><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>j</mi><mo>^</mo></mover><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><mover accent="true"><mi>b</mi><mo>→</mo></mover><mo>=</mo><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>+</mo><mn>2</mn><mover accent="true"><mi>j</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>k</mi><mo>^</mo></mover><mo>.</mo></mrow></math> Let <math><mrow><mover accent="true"><mi>c</mi><mo>→</mo></mover></mrow></math> be vector satisfying <math><mrow><mover accent="true"><mi>a</mi><mo>→</mo></mover><mo>×</mo><mrow><mo>(</mo><mrow><mover accent="true"><mi>b</mi><mo>→</mo></mover><mo>×</mo><mover accent="true"><mi>c</mi><mo>→</mo></mover></mrow><mo>)</mo></mrow><mo>=</mo><mover accent="true"><mi>b</mi><mo>→</mo></mover><mo>+</mo><mi>λ</mi><mover accent="true"><mi>c</mi><mo>→</mo></mover><mo>.</mo></mrow></math> If <math><mrow><mover accent="true"><mi>b</mi><mo>→</mo></mover><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><mover accent="true"><mi>c</mi><mo>→</mo></mover></mrow></math> are non-parallel, then the value of <math><mrow><mi>λ</mi></mrow></math> is:</strong></p>

(a? .c? )b? ? (a? .b? )c? =b? +? c? (given)a? .c? =1, ? =? a? .b? ? =? (3, 1, 0). (1, 2, 1)= (3 + 2)= 5

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Let $\vec{a} = 3 \hat{i} + \hat{j} a n d \vec{b} = \hat{i} + 2 \hat{j} + \hat{k} .$ Let $\vec{c}$ be vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + λ \vec{c} .$ If $\vec{b} a n d \vec{c}$ are non-parallel, then the value of $λ$ is:

Option 1 -

Option 2 -

Option 3 -

Option 4 -

3 Views | Posted 2 months ago

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$(\overset{?}{a} . \overset{?}{c}) \overset{?}{b} ? (\overset{?}{a} . \overset{?}{b}) \overset{?}{c}$

$= \overset{?}{b} + ? \overset{?}{c} (g i v e n)$

$\overset{?}{a} . \overset{?}{c} = 1, ? = ? \overset{?}{a} . \overset{?}{b}$

$? = ? (3, 1, 0) . (1, 2, 1)$

= (3 + 2)= 5

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