Vector A- and B- are mutually perpendicular- Component of A- - B- in the direction of A- - B- will be -

The correct option is C A ^ 2 B ^ 2 √( A ^ 2 + B ^ 2 ) Unit vertor along #10;A⃗ B⃗ #10; #10; ⇒#10;A B⃗|A⃗ B⃗| = A⃗ B⃗√(A^2 ...

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Byju's Answer

Standard XII

Physics

Vector Component

Vector A⃗ a...

Question

Vector $\to A$ and $\to B$ are mutually perpendicular. Component of $\to A + \to B$ in the direction of $\to A - \to B$ will be -

\frac{A^{2} + B^{2}}{\sqrt{A^{2} - B^{2}}}

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\sqrt{A^{2} - B^{2}}

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\frac{A + B}{A - B}

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\frac{A^{2} - B^{2}}{\sqrt{A^{2} + B^{2}}}

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Solution

The correct option is C $\frac{A^{2} - B^{2}}{\sqrt{A^{2} + B^{2}}}$
$Unit vertor along \to A - \to B$

$\Rightarrow \frac{\to A - \to B}{| \to A - \to B |} = \frac{\to A - \to B}{\sqrt{A^{2} + B^{2}}}$

$So, component of \to A + \to B along \to A - \to B$

$(\to A + \to B) \cdot \frac{(\to A - \to B)}{\sqrt{A^{2} + B^{2}}} = \frac{A^{2} - B^{2}}{\sqrt{A^{2} + B^{2}}}$

Hence, correct option is option d.

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Vector →A and →B are mutually perpendicular. Component of →A+→B in the direction of →A−→B will be -

The correct option is C A2−B2√A2+B2Unit vertor along →A−→B ⇒→A−→B|→A−→B|=→A−→B√A2+B2 So, component of →A+→B along →A−→B (→A+→B)⋅(→A−→B)√A2+B2=A2−B2√A2+B2 Hence, correct option is option d.

Vector $\to A$ and $\to B$ are mutually perpendicular. Component of $\to A + \to B$ in the direction of $\to A - \to B$ will be -