The position vectors of points A, B, C and D | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The displacement vector $\overrightarrow{AB}$ is calculated as: $\overrightarrow{AB} = \vec{B} - \vec{A} = (4\hat{i} + 5\hat{j} + 6\hat{k}) - (3\h

Vedclass · Accepted Answer

Antiparallel

Vedclass · Answer

(B) The displacement vector $\overrightarrow{AB}$ is calculated as: $\overrightarrow{AB} = \vec{B} - \vec{A} = (4\hat{i} + 5\hat{j} + 6\hat{k}) - (3\hat{i} + 4\hat{j} + 5\hat{k}) = \hat{i} + \hat{j} + \hat{k}$.The displacement vector $\overrightarrow{CD}$ is calculated as: $\overrightarrow{CD} = \vec{D} - \vec{C} = (4\hat{i} + 6\hat{j}) - (7\hat{i} + 9\hat{j} + 3\hat{k}) = -3\hat{i} - 3\hat{j} - 3\hat{k}$.We can rewrite $\overrightarrow{CD}$ as: $\overrightarrow{CD} = -3(\hat{i} + \hat{j} + \hat{k}) = -3\overrightarrow{AB}$.Since $\overrightarrow{CD} = k\overrightarrow{AB}$ where $k = -3$ (a negative scalar),the vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are antiparallel.

The position vectors of points $A, B, C$ and $D$ are $A = 3\hat{i} + 4\hat{j} + 5\hat{k}$,$B = 4\hat{i} + 5\hat{j} + 6\hat{k}$,$C = 7\hat{i} + 9\hat{j} + 3\hat{k}$ and $D = 4\hat{i} + 6\hat{j}$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

Similar Questions

If water at $100^\circ C$ cools in $10$ minutes to $80^\circ C$ and to $65^\circ C$ in the next $10$ minutes, then the room temperature will be ...

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

Which of the following relations is correct?

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence,the forces $\vec{A}$ and $\vec{B}$ are

The magnitude of the vector $|2\hat{i} - \hat{j} - 5\hat{k}|$ is .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module