The orthogonal projection of 3 -2 -5 k- on a vector perpendicular to 2 -2 k- isA- 13-3-4-3-11-3k-B- 13-3-4-3-11-3k-C- 13-3-4-3-11-3k-D- 13-3-4-3-11-3k-

The correct option is A 13/3î+4/3ĵ 11/3k̂ Orthogonal projection =3î+2ĵ 5k̂ (3î+2ĵ 5k̂).(2î ĵ+2k̂)/4+1+4(2î ĵ+k̂) =(3î+2ĵ 5k̂) 6 2 10/9(2î ĵ+2k̂)=(3î+2ĵ 5k̂)+2 ...

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Byju's Answer

Standard IX

Mathematics

Applications of Dot Product

The orthogona...

Question

The orthogonal projection of $3^i + 2^j - 5^k$ on a vector perpendicular to $2^i -^j + 2^k$ is

\frac{13}{3}^i + \frac{4}{3}^j - \frac{11}{3}^k

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\frac{13}{3}^i + \frac{4}{3}^j - \frac{11}{3}^k

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\frac{13}{3}^i + \frac{4}{3}^j + \frac{11}{3}^k

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\frac{13}{3}^i - \frac{4}{3}^j - \frac{11}{3}^k

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Solution

The correct option is A $\frac{13}{3}^i + \frac{4}{3}^j - \frac{11}{3}^k$

Orthogonal projection $= 3^i + 2^j - 5^k - \frac{(3^i + 2^j - 5^k) . (2^i -^j + 2^k)}{4 + 1 + 4} (2^i -^j +^k)$
$= (3^i + 2^j - 5^k) - \frac{6 - 2 - 10}{9} (2^i -^j + 2^k) = (3^i + 2^j - 5^k) + \frac{2}{3} (2^i -^j + 2^k) = \frac{13^i + 4^j - 11^k}{3}$

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