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JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

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Analyzing +4 | -1

Let the position vectors of the points

A, B, C

and

D

be

5 \hat{i}+5 \hat{j} +2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}

and

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

. Let the set

S=\{\lambda \in \mathbb{R}

: the points

A

,

B, C

and

D

are coplanar}. Then

\sum\limits_{{\lambda \in S}}(\lambda+2)^{2}

is equal to

View answer and explanation

Correct option: D

41

The correct answer is D (41) because the sum of

(\lambda+2)^2

for the values of

\lambda

that make the points coplanar is 41.

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

unit vector such that

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

\mathbf{d}

is equal to
A vector

{\mathbf{\vec a}}

2\;p

and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense, if this respect to new system

{\mathbf{\vec a}}

p + 1

\vec{a}, \vec{b}

\vec{c}

are three mutually perpendicular unit vetors and

\vec{d}

is a unit vector which makes equal angles with

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

\overrightarrow{\mathrm{c}}

then the value of

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

The non-zero vectors are

\vec{a}, \vec{b}

\vec{c}

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

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

. Then the angle between

\vec{a}

\vec{c}

is If the vectors

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

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

ar coplanar, then the value of

\lambda

is equal The medium

AD

of the triangle

ABC

E,\;BE

AC

F

AF:AC =