Let a,b and c be three vectors such that ${\rm{a}}\,{\rm{ = }}\,{\rm{b \times }}\,{\rm{(b \times c)}}{\rm{.}}$ . If magnitude of the vectors a, b and c are $\sqrt 2 ,\,\,1\,\,{\rm{and}}\,\,2$, respectively and the angle between b and c is $\theta \,\,\left( {0 < \theta < \frac{\pi }{2}} \right)\,$, then the Value of $(1 + \tan \theta )$ is equal to

$\frac{{\sqrt 3 + 1}}{{\sqrt 3 }}$

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Application +4 | -1

Let a,b and c be three vectors such that

\mathrm{a}\,\mathrm{ = }\,\mathrm{b \times }\,\mathrm{(b \times c)}\mathrm{.}

. If magnitude of the vectors a, b and c are

\sqrt 2 ,\,\,1\,\,\mathrm{and}\,\,2

, respectively and the angle between b and c is

\theta \,\,\left( {0 < \theta < \frac{\pi }{2}} \right)\,

, then the Value of

(1 + \tan \theta )

is equal to

View answer and explanation

Correct option: B

Option B (2) is correct. The problem involves vector algebra and trigonometric identities, where the angle between vectors b and c is found to be π/4, leading to 1 + tan(θ) = 2.

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