JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Analyzing +4 | -1

Let the cosine of angle between the vectors

\mathrm{p}

and

\mathbf{q}

\lambda

such that

2 \mathbf{p}+\mathbf{q}=\hat{\mathbf{i}}+\hat{\mathbf{j}}

and

\mathbf{p}+2 \mathbf{q}=\hat{\mathbf{i}}-\hat{\mathbf{j}}

, then

\lambda

is equal to

View answer and explanation

Correct option: B

-\frac{4}{5}

The correct answer is B (-

\frac{4}{5}

) because the cosine of the angle between the vectors p and q is calculated using the given equations and the dot product formula.

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\frac{\text { Projection of vector } \mathbf{a} \text { on vector } \mathbf{b}}{\text { Projection of vector } \mathbf{b} \text { on vector } \mathbf{a}}

{\mathbf{\vec a}}

{\mathbf{\vec b}}

\frac{{5\pi }}{6}

{\mathbf{\vec a}}

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\frac{{ - 6}}{{\sqrt 3 }}

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\frac{1}{4} \mathrm{~m} / \mathrm{s}

O A

O B

30^{\circ}

45^{\circ}

O B

2x + 4y - 5z = 10