If $$3$$,−$$1$$,$$2$$,$$4$$,$$1$$,$$0are$$ the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

Question

If  $$3$$,−$$1$$,$$2$$,$$4$$,$$1$$,$$0are$$ the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

Infinity Learn · Accepted Answer

If  $$a1$$,$$b1$$,$$c1$$,$$a2$$,$$b2$$,$$c2are$$ direction ratios of two lines. The direction ratios of any line perpendicular to the above two lines are proportional to the components of the vectors two whose direction ratios $$areijka1b1c1a2b2c2$$  Hence,$$ijka1b1c1a2b2c2=ijk3$$−$$12410=i$$−$$2$$−j−$$8+k7Therefore$$, the direction ratios of perpendicular line are proportional to  −$$2$$,$$8$$,$$7It$$ implies that $$32$$,$$128$$,$$112are$$ not proportional to the above direction ratios.

If $(3, - 1, 2), (4, 1, 0)$ are the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

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If 3,−1,2,4,1,0are the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?

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If $(3, - 1, 2), (4, 1, 0)$ are the direction ratios of two straight lines, then which of the following are not direction numbers perpendicular to both these lines?