The distance of the point $$-i$$¯$$+2j$$¯$$+6k$$¯ from the straight line through the point (2$$,$$3$$,$$-4) and parallel to $$6i$$¯$$+3j$$¯$$-4k$$¯ is

Question

The distance of the point $$-i$$¯$$+2j$$¯$$+6k$$¯ from the straight line through the point (2$$,$$3$$,$$-4) and  parallel to $$6i$$¯$$+3j$$¯$$-4k$$¯ is

Infinity Learn · Accepted Answer

[$$SolutionStep1$$]:From the figure Dr's of AP→$$=(-3$$,$$-1$$,$$10)$$  $$x2-x1$$,$$y2-y1$$,$$z2-z1$$[$$SolutionStep2$$]:AP→$$=110PN$$¯ vector is perpendicular to the line [$$SolutionStep3$$]:AN→$$=$$ The projection of AP→ one the line $$(on(6$$,$$3$$,$$-4))=AP$$→$$.6$$,$$3$$,−$$46$$,$$3$$,−$$4=$$−$$3$$,−$$1$$,$$10.6$$,$$3$$,−$$46$$,$$3$$,−$$4=$$−$$18$$−$$3$$−$$4061=61$$ From figure $$PN2=AP2-AN2=110$$−$$61=49$$⇒$$PN=7$$

$The distance of the point - \bar{i} + 2 \bar{j} + 6 \bar{k} from the straight line through the point (2, 3, - 4) and$ $parallel to 6 \bar{i} + 3 \bar{j} - 4 \bar{k} is$

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The distance of the point -i¯+2j¯+6k¯ from the straight line through the point (2,3,-4) and parallel to 6i¯+3j¯-4k¯ is

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$The distance of the point - \bar{i} + 2 \bar{j} + 6 \bar{k} from the straight line through the point (2, 3, - 4) and$ $parallel to 6 \bar{i} + 3 \bar{j} - 4 \bar{k} is$