Question:medium
The vector with terminal point \( A(2, -3, 5) \) and initial point \( B(3, -4, 7) \) is:
The vector with terminal point \( A(2, -3, 5) \) and initial point \( B(3, -4, 7) \) is:
Show Hint
To find the vector between two points, subtract the coordinates of the initial point from the corresponding coordinates of the terminal point:
\[
\vec{v} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k}.
\]
Updated On: Jan 13, 2026
- \( \hat{i} - \hat{j} + 2\hat{k} \)
- \( \hat{i} + \hat{j} + 2\hat{k} \)
- \( -\hat{i} - \hat{j} - 2\hat{k} \)
- \( -\hat{i} + \hat{j} - 2\hat{k} \)
Show Solution
The Correct Option is D
Solution and Explanation
The vector from \( B(3, -4, 7) \) to \( A(2, -3, 5) \) is computed as \( \vec{v} = \vec{A} - \vec{B} \). The components are \( \vec{v} = (2 - 3)\hat{i} + (-3 - (-4))\hat{j} + (5 - 7)\hat{k} \). Simplifying yields \( \vec{v} = (-1)\hat{i} + (1)\hat{j} + (-2)\hat{k} \), which is \( \vec{v} = -\hat{i} + \hat{j} - 2\hat{k} \). The vector is \( -\hat{i} + \hat{j} - 2\hat{k} \), corresponding to option (D).
Was this answer helpful?
0
Top Questions on Vector Algebra
- If $\overrightarrow{AB}=\hat{j}+\hat{k}$ and $\overrightarrow{AC}=3\hat{i}-\hat{j}+4\hat{k}$ represent the two vectors along the sides $AB$ and $AC$ of $\triangle ABC$, prove that the median $\overrightarrow{AD}=\dfrac{\overrightarrow{AB}+\overrightarrow{AC}}{2}$ where $D$ is the midpoint of $BC$. Hence, find the length of the median $AD$.
- CBSE Class XII - 2026
- Mathematics
- Vector Algebra
- For two vectors $\vec a$ and $\vec b$
Assertion (A): $|\vec a\times \vec b|^2+(\vec a\cdot \vec b)^2=|\vec a|^2|\vec b|^2$
Reason (R): $|\vec a\times \vec b|=|\vec a||\vec b|\sin\theta$, where $\theta$ is the angle between them.- CBSE Class XII - 2026
- Mathematics
- Vector Algebra
- If $|\vec a|=5$ and $-2\le \lambda \le 1$, then the sum of the greatest and the smallest value of $|\lambda \vec a|$ is
- CBSE Class XII - 2026
- Mathematics
- Vector Algebra
- The value of expression \(\hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} + \hat{k} \times \hat{k}\) is
- UP Board XII - 2026
- Mathematics
- Vector Algebra
- Want to practice more? Try solving extra ecology questions todayView All Questions
