If A4, 3, 5, B6, 4, 3, C2, -1, 4, D0, 1, 5 then the projection of AB___ on CD___ is

The given points are A4, 3, 5, B6, 4, 3, C2, -1, 4, D0, 1, 5Direction ratios of line AB¯ are x2-x1,y2-y1,z2-z1=2,1,-2Direction rations of CD⇀ are -2,2,1Direction cosines of CD⇀ are -2,2,1Projection of AB___ on CD___ =-236-4+234-3+133-5=13-4+2-2=-43.

If A4, 3, 5, B6, 4, 3, C2, -1, 4, D0, 1, 5 then the projection of AB___ on CD___ is

The given points are A4, 3, 5, B6, 4, 3, C2, -1, 4, D0, 1, 5Direction ratios of line AB¯ are x2-x1,y2-y1,z2-z1=2,1,-2Direction rations of CD⇀ are -2,2,1Direction cosines of CD⇀ are -2,2,1Projection of AB___ on CD___ =-236-4+234-3+133-5=13-4+2-2=-43.

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If $A (4, 3, 5), B (6, 4, 3), C (2, - 1, 4), D (0, 1, 5)$ then the projection of $\overset{_}{A B}$ on $\overset{_}{C D}$ is

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$\frac{3}{4}$

$- \frac{4}{3}$

$- \frac{3}{4}$

answer is C.

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Detailed Solution

The given points are $A (4, 3, 5), B (6, 4, 3), C (2, - 1, 4), D (0, 1, 5)$

Direction ratios of line $\bar{A B}$ are $<x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1}> = <2, 1, - 2>$

Direction rations of $\overset{⇀}{C D}$ are $<- 2, 2, 1>$

Direction cosines of $\overset{⇀}{C D}$ are $<- 2, 2, 1>$

Projection of $\overset{___}{A B}$ on $\overset{___}{C D}$ $= - \frac{2}{3} (6 - 4) + \frac{2}{3} (4 - 3) + \frac{1}{3} (3 - 5) = \frac{1}{3} (- 4 + 2 - 2) = - \frac{4}{3} .$