JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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The position vectors of three consecutive vertices of a parallelogram are

\mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{i}+3 \mathbf{j}+5 \mathbf{k}

and

7 \mathbf{i}+9 \mathbf{j}+11 \mathbf{k}

. The position vector of the fourth vertex is

View answer and explanation

Correct option: B

7(\mathbf{i}+\mathbf{j}+\mathbf{k})

The correct answer is D (

6 \mathbf{i}+8 \mathbf{j}+10 \mathbf{k}

) because in a parallelogram, the midpoints of the diagonals coincide, allowing us to solve for the fourth vertex.

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 =