The orthogonal projection vector of a-2-k- on b - 4- -4-7k- is-

Orthogonal projection vector of a on b = a. b|b|^2b = (î 2ĵ+k̂).(4î 4ĵ+7k̂)(√(16+16+49))^2(4î 4ĵ+7k̂) = (4+8+7)81(4î 4ĵ+7k̂) =1981 nbsp;(4î 4ĵ+7k̂) ...

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Standard XII

Physics

Vectors and Its Types

The orthogona...

Question

The orthogonal projection vector of $\to a =^i - 2^j +^k$ on $\to b = 4^i - 4^j + 7^k$ is:

\frac{17}{9} (4^i + 4^j - 7^k)

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\frac{19}{9} (4^i - 4^j + 7^k)

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\frac{17}{81} (4^i + 4^j - 7^k)

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\frac{19}{81} (4^i - 4^j + 7^k)

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Solution

The correct option is D $\frac{19}{81} (4^i - 4^j + 7^k)$
orthogonal projection vector of $\to a$ on $\to b = \frac{\to a . \to b}{| \to b |^{2}} \to b$
$= \frac{(^i - 2^j +^k) . (4^i - 4^j + 7^k)}{(\sqrt{16 + 16 + 49})^{2}} (4^i - 4^j + 7^k)$
$= \frac{(4 + 8 + 7)}{81} (4^i - 4^j + 7^k) = \frac{19}{81} (4^i - 4^j + 7^k)$

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Vectors and Its Types

Standard XII Physics

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The orthogonal projection vector of →a=^i−2^j+^k on →b=4^i−4^j+7^k is:

The correct option is D 1981(4^i−4^j+7^k)orthogonal projection vector of →a on →b=→a.→b|→b|2→b =(^i−2^j+^k).(4^i−4^j+7^k)(√16+16+49)2(4^i−4^j+7^k) =(4+8+7)81(4^i−4^j+7^k)=1981(4^i−4^j+7^k)

The orthogonal projection vector of $\to a =^i - 2^j +^k$ on $\to b = 4^i - 4^j + 7^k$ is: