$$A1$$,$$2$$,$$3$$,$$B4$$,$$5$$,$$7$$,C−$$4$$,$$3$$,−$$6$$,$$D2$$,$$k2$$,$$2$$ are four points. If the lines AB→ and CD→ are parallel, then $$k=$$

Question

$$A1$$,$$2$$,$$3$$,$$B4$$,$$5$$,$$7$$,C−$$4$$,$$3$$,−$$6$$,$$D2$$,$$k2$$,$$2$$ are four points. If the lines AB→ and CD→ are parallel, then $$k=$$

Infinity Learn · Accepted Answer

If two lines are parallel, then their direction ratios are in proportional The direction ration of line joining $$Ax1$$,$$y1$$,$$z1$$ and $$Bx2$$,$$y2$$,$$z2$$ is $$x2$$−$$x1$$,$$y2$$−$$y1$$,$$z2$$−$$z1The$$ direction ration of line joining $$A1$$,$$2$$,$$3$$ and $$B4$$,$$5$$,$$7$$ $$is3$$,$$3$$,$$4The$$ direction ration of line joining C−$$4$$,$$3$$,−$$6$$ and $$D2$$,$$k2$$,$$2$$ $$is6$$,$$k2$$−$$3$$,$$8Since$$ the lines are parallel, their direction ratios are proportional. It implies $$that63=k2$$−$$33=84Therefore$$, $$k2$$−$$3=6$$⇒$$k2=9$$⇒$$k=$$±$$3$$

$A (1, 2, 3), B (4, 5, 7), C (- 4, 3, - 6), D (2, k^{2}, 2)$ are four points. If the lines $\vec{A B} and \vec{C D}$ are parallel, then $k =$

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A1,2,3,B4,5,7,C−4,3,−6,D2,k2,2 are four points. If the lines AB→ and CD→ are parallel, then k=

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$A (1, 2, 3), B (4, 5, 7), C (- 4, 3, - 6), D (2, k^{2}, 2)$ are four points. If the lines $\vec{A B} and \vec{C D}$ are parallel, then $k =$