JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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Application +4 | -1

The position vectors of the points

A, B, C

and

D

are

3 {i}-2 {j}-{k}, 2 {i}+3 {j}-4 {k},-{i}+{j}+2 {k}

and

4 {i}+5 {j}+\lambda {k}

respectively. If the points

{A}, {B}, {C}

and

{D}

are on a plane, then the value of

\lambda

View answer and explanation

Correct option: B

\frac{-146}{17}

Option B (

\frac{{-146}}{{17}}

) is correct because the points are coplanar if the scalar triple product of the vectors formed by the points is zero, leading to the given value of

\lambda

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 =