The points (5$$,$$2$$,$$4),(6$$,$$-$$ $$1$$,$$2) and (8$$, $$-$$ $$7$$, $$k) are collinear, if k is equal to

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Now,Δ$$xy=125216$$−$$118$$−$$71=12$$|[$$5($$−$$1+7)$$−$$2(6$$−$$8)+1($$−$$42+8)$$]|$$=12$$|[$$30+4$$−$$34$$]|$$=0$$Δ$$yz=12241$$−$$121$$−$$7k1=12$$|[$$2(2$$−$$k)$$−$$4($$−$$1+7)+1($$−$$k+14)$$]|$$=12$$|[$$4$$−$$2k$$−$$24$$−$$k+14$$]|$$=12$$|[−$$3k$$−$$6$$]|$$=3k+62$$Δ$$zx=12451261k81=12$$|[$$4(6$$−$$8)$$−$$5(2$$−$$k)+1(16$$−$$6k)$$]|$$=12$$|[−$$8$$−$$10+5k+16$$−$$6k$$]|$$=12$$|[−$$2$$−k]|$$=k+22For$$ collinear  ∆$$=0$$∴    $$02+3k+622+k+222$$    $$=0$$⇒    $$14(3k+6)2+(k+2)2$$    $$=0$$⇒    $$9k2+36+36k+k2+4+4k=0$$⇒    $$10k2+40k+40=0$$⇒$$k2+4k+4=0$$⇒        $$(k+2)2=0$$⇒$$k=$$−$$2$$

The points (5,2,4),(6,- 1,2) and (8, - 7, k) are collinear, if k is equal to

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