If the angle between the vectors λ$$i^$$−$$3j^+5k^$$ and $$2$$λ$$i^$$−λ$$j^$$−$$k^$$ is an obtuse angle and λ is an integer, then the number of $$value(s)$$ of λ $$is/are$$

Question

If the angle between the vectors λ$$i^$$−$$3j^+5k^$$ and $$2$$λ$$i^$$−λ$$j^$$−$$k^$$ is an obtuse angle and λ  is an integer, then the number of $$value(s)$$ of λ $$is/are$$

Infinity Learn · Accepted Answer

Let a¯$$=$$λ$$i^$$−$$3j^+5k^$$ and b¯$$=2$$λ$$i^$$−λ$$j^$$−$$k^$$ The angle between the vector a¯ and b¯ is an obtuse angle then a¯⋅b¯<$$0$$⇒$$($$λ$$i^$$−$$3j^+5k^)$$⋅(2$$λ$$i^$$−λ$$j^$$−$$k^)<$$0$$⇒$$2$$λ$$2+3$$λ−$$5$$<$$0$$⇒(2$$λ$$+5)($$λ−$$1)<$$0$$⇒λ∈−$$52$$,$$1$$ Integer values of λ are −$$2$$,−$$1$$,$$0$$ Hence, the number of values of λ is $$3Therefore$$, the correct answer $$is(1)$$.

$If the angle between the vectors λ \hat{i} - 3 \hat{j} + 5 \hat{k} and 2 λ \hat{i} - λ \hat{j} - \hat{k} is an obtuse angle and λ$ $is an integer, then the number of value(s) of λ is/are$

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If the angle between the vectors λi^−3j^+5k^ and 2λi^−λj^−k^ is an obtuse angle and λ is an integer, then the number of value(s) of λ is/are

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$If the angle between the vectors λ \hat{i} - 3 \hat{j} + 5 \hat{k} and 2 λ \hat{i} - λ \hat{j} - \hat{k} is an obtuse angle and λ$ $is an integer, then the number of value(s) of λ is/are$