JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Application +4 | -1

Let

\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=2 \hat{i}+3 \hat{j}-5 \hat{k}

and

\overrightarrow{{c}}=3 \hat{{i}}-\hat{{j}}+\lambda \hat{{k}}

be three vectors. Let

\overrightarrow{{r}}

be a unit vector along

\vec{b}+\vec{c}.

\vec{r} \cdot \vec{a}=3,

then

3 \lambda

is equal to:

View answer and explanation

Correct option: B

Option B (25) is correct because by finding the unit vector along

\vec{b}+\vec{c}

and using the dot product condition, we can solve for

\lambda

and find that

3\lambda = 25

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O A

O B

30^{\circ}

45^{\circ}

O B

2x + 4y - 5z = 10