Suppose ${\bf{\vec a}} = \lambda \;\widehat {\bf{i}} - 7\widehat {\bf{j}} + 3{\bf{\hat k}}$, ${\bf{\vec b}} = \lambda \;\widehat {\bf{i}} + \widehat {\bf{j}} + 2\lambda \;{\bf{\hat k}}.$ If the angle between ${{\bf{\vec a}}}$ and ${{\bf{\vec b}}}$ is grater than $90^\circ $, then λ satisfies the inequality

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

1 of 1

Application +4 | -1

Suppose

\mathbf{\vec a} = \lambda \;\widehat \mathbf{i} - 7\widehat \mathbf{j} + 3\mathbf{\hat k}

\mathbf{\vec b} = \lambda \;\widehat \mathbf{i} + \widehat \mathbf{j} + 2\lambda \;\mathbf{\hat k}.

If the angle between

{\mathbf{\vec a}}

and

{\mathbf{\vec b}}

is grater than

90^\circ

, then λ satisfies the inequality

View answer and explanation

Correct option: A

- 7 < \lambda < 1

The correct answer is A. The angle between two vectors is greater than 90 degrees when their dot product is negative, leading to the inequality

- 7 < \lambda < 1

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O A

O B

30^{\circ}

45^{\circ}

O B

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