Let <math> <mrow> <mover accent="true"> <mi>a</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> <mn>3</mn> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> <mo>,</mo> <mtext> </mtext> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>k</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> be a vector such that <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"> <mn>0</mn> <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> <mtext> </mtext> <mo>.</mo> <mtext> </mtext> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mo>=</mo> <mn>5</mn> <mo>.</mo> </mrow> </math> Then, the value of <math> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mtext> </mtext> <mo>.</mo> <mtext> </mtext> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> </math> is equal to……….

Data contradiction. a → × ( b → × c → ) = ( a → ⋅ c → ) b → − ( a → ⋅ b → ) c →

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Let $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k} a n d \vec{c}$ be a vector such that $\vec{a} + (\vec{b} \times \vec{c}) = \vec{0} a n d \vec{b} . \vec{c} = 5 .$ Then, the value of $3 (\vec{c} . \vec{a})$ is equal to……….

2 Views | Posted 2 weeks ago

Answered by

Vishal Baghel | Contributor-Level 10

2 weeks ago

Data contradiction.

$\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}$

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