Let $A = (- 3, 4, - 8)$ and $B = (5, - 6, 4)$ , then the coordinates of the point in which the $X Y$ - plane or $X O Y$ plane divides the line segment $A B$ is

(7, - 8, 0)

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(\frac{7}{3}, - \frac{8}{3}, 0)

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(\frac{7}{2}, - \frac{8}{2}, 0)

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(0, \frac{7}{3}, - \frac{8}{3})

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Solution

The correct option is A $(\frac{7}{3}, - \frac{8}{3}, 0)$
Let $\to O$ divide $A B$ into $K : 1$
By Section Formula
$(x, y, o) = \frac{K B + A}{K + 1}$
$(x, y, o) = \frac{K (5, - 6, 4) + (- 3, 4, - 8)}{K + 1}$
$0 = \frac{K (4) - 8}{K + 1}$
$K = 2$

$x = \frac{10 - 3}{3} = \frac{7}{3}$

$y = \frac{- 12 + 4}{3} = \frac{- 8}{3}$

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Let A=(−3,4,−8) and B=(5,−6,4), then the coordinates of the point in which the XY- plane or XOY plane divides the line segment AB is

The correct option is A (73,−83,0)Let →O divide AB into K:1By Section Formula(x,y,o)=KB+AK+1 (x,y,o)=K(5,−6,4)+(−3,4,−8)K+10=K(4)−8K+1K=2x=10−33=73y=−12+43=−83

Let $A = (- 3, 4, - 8)$ and $B = (5, - 6, 4)$ , then the coordinates of the point in which the $X Y$ - plane or $X O Y$ plane divides the line segment $A B$ is