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

|A | = √(2^2+ 3^2 +( 1)^1) = √(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 on B = A. B ...

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Byju's Answer

Standard XIII

Physics

Multiplication with Vectors

If A = 2î+ 3ĵ...

Question

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

\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 $\frac{3}{\sqrt{26}}$
$| \to A | = \sqrt{2^{2} + 3^{2} + (- 1)^{1}} = \sqrt{4 + 9 + 1} = \sqrt{14}$
$| \to B | = \sqrt{(- 1)^{2} + 3^{2} + (4)^{2}} = \sqrt{1 + 9 + 16} = \sqrt{26}$
$\to A . \to B = 2 (- 1) + 3 \times 3 + (- 1) (4) = 3$
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

The correct option is B 3√26|→A|=√22+32+(−1)1=√4+9+1=√14 |→B|=√(−1)2+32+(4)2=√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 $\to A on \to B$