JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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A unit vector is orthogonal to

5 \hat{i}+2 \hat{j}+6 \hat{k}

and is coplanar to

2 \hat{i}+\hat{j}+\hat{k}

and

\hat{i}-\hat{j}+\hat{k}

then the vector is

View answer and explanation

Correct option: A

\frac{3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{10}}

Option A (

\frac{3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{10}}

) is correct. By setting up a linear combination of the coplanar vectors and using the orthogonality condition, we can solve for the unit vector.

More Questions from ADDITION OF VECTORS

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\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}

\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}

\mathbf{d}

a

\mathbf{a} \cdot \mathbf{d}=0=(b \mathbf{c}

\mathbf{d}

{\mathbf{\vec a}}

2\;p

{\mathbf{\vec a}}

p + 1

\vec{a}, \vec{b}

\vec{c}

\vec{d}

\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}

\overrightarrow{\mathrm{c}}

|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|^2

\vec{a}, \vec{b}

\vec{c}

\vec{a}=8 \vec{b}

\vec{c}=-7 \vec{b}

\vec{a}

\vec{c}

2 \mathbf{i}+\mathbf{j}-\mathbf{k},-\mathbf{i}+2 \mathbf{j}+\lambda \mathbf{k}

-5 \mathbf{i}+2 \mathbf{j}-\mathbf{k}

\lambda

AD

ABC

E,\;BE

AC

F

AF:AC =