If A - 2-3-k- and B - -3-4k- then projection of A on B will be

|A| = √(2^2 + 3^2 + ( 1)^2) = √(4 + 9 + 1) = √(14) |B| = √(( 1)^2 + 3^2 + 4^2) = √(1 + 9 + 16) = √(26) A . B = 2( 1) + 3 × 3 + ( 1)(4) = 3 The projection of A o ...

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Byju's Answer

Standard XIII

Physics

Vector Component

If A = 2î+3ĵ-...

Question

If $\to A = 2^i + 3^j -^k$ and $\to B = -^i + 3^j + 4^k$ , then projection of $\to A$ on $\to B$ will be

\frac{3}{\sqrt{13}}

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\frac{3}{\sqrt{26}}

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\sqrt{\frac{3}{26}}

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\sqrt{\frac{3}{13}}

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Solution

The correct option is B $\frac{3}{\sqrt{26}}$
$| \to A | = \sqrt{2^{2} + 3^{2} + (- 1)^{2}} = \sqrt{4 + 9 + 1} = \sqrt{14}$
$| \to B | = \sqrt{(- 1)^{2} + 3^{2} + 4^{2}} = \sqrt{1 + 9 + 16} = \sqrt{26}$
$\to A . \to B = 2 (- 1) + 3 \times 3 + (- 1) (4) = 3$
The projection of $\to A$ on $\to B = \frac{\to A . \to B}{| \to B |}$
$= \frac{3}{\sqrt{26}}$

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If →A=2^i+3^j−^k and →B=−^i+3^j+4^k, then projection of →A on →B will be

The correct option is B 3√26|→A|=√22+32+(−1)2=√4+9+1=√14 |→B|=√(−1)2+32+42=√1+9+16=√26 →A.→B=2(−1)+3×3+(−1)(4)=3 The projection of →A on →B=→A.→B|→B| =3√26

If $\to A = 2^i + 3^j -^k$ and $\to B = -^i + 3^j + 4^k$ , then projection of $\to A$ on $\to B$ will be