For A 1-2-4- B 5-1-7- C 3-6-2- D 4-5-1- the projection of AB on CD isA- 2 -3-2 -3- 2 -3- 3-134-1-3C- 1-1-1D- 2-2-2

The correct option is D (2, 2,2)AB=4î+ĵ+3k̂ CD=î ĵ+k̂ Hence, the projection of nbsp;AB on nbsp;CD is nbsp; (AB.CD|CD|).ĈD̂ =(4 1+3√(1+1+1)).(î ĵ+k̂√(1+1+ ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Complex Numbers

For A 1,-2,4,...

Question

For $A (1, - 2, 4), B (5, - 1, 7), C (3, 6, - 2), D (4, 5, - 1)$ , the projection of $- - \to A B$ on $- - \to C D$ is

(2 \sqrt{3}, - 2 \sqrt{3}, 2 \sqrt{3})

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\frac{3}{13} (4, 1, 3)

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(1, - 1, 1)

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(2, - 2, 2)

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Solution

The correct option is D $(2, - 2, 2)$
$- - \to A B = 4^i +^j + 3^k$
$- - \to C D =^i -^j +^k$
Hence, the projection of $- - \to A B$ on $- - \to C D$ is
$⎛ ⎜ ⎝ \frac{- - \to A B . - - \to C D}{| - - \to C D |} ⎞ ⎟ ⎠ .^C D$
$= (\frac{4 - 1 + 3}{\sqrt{1 + 1 + 1}}) . (\frac{^i -^j +^k}{\sqrt{1 + 1 + 1}})$
$= 2^i - 2^j + 2^k$

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For A(1,−2,4), B(5,−1,7), C(3,6,−2), D(4,5,−1), the projection of −−→AB on −−→CD is

The correct option is D (2,−2,2)−−→AB=4^i+^j+3^k −−→CD=^i−^j+^k Hence, the projection of −−→AB on −−→CD is ⎛⎜⎝−−→AB.−−→CD|−−→CD|⎞⎟⎠.^CD =(4−1+3√1+1+1).(^i−^j+^k√1+1+1) =2^i−2^j+2^k

For $A (1, - 2, 4), B (5, - 1, 7), C (3, 6, - 2), D (4, 5, - 1)$ , the projection of $- - \to A B$ on $- - \to C D$ is