Question:
If the component of one vector in the direction of another vector is zero, then those two vectors are
If the component of one vector in the direction of another vector is zero, then those two vectors are
Show Hint
Zero projection (component) always implies orthogonality ($90^{\circ}$).
Updated On: Jul 4, 2026
- parallel to each other
- perpendicular to each other
- opposite to each other
- coplanar vectors
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
The component of vector $\vec{A}$ in the direction of $\vec{B}$ is given by $A \cos \theta$, where $\theta$ is the angle between them.
Step 2: Meaning
If the component is zero, then $A \cos \theta = 0$. Since the magnitude $A$ is non-zero, $\cos \theta$ must be zero.
Step 3: Analysis
The cosine of an angle is zero when the angle $\theta = 90^{\circ}$.
Step 4: Conclusion
An angle of $90^{\circ}$ means that the two vectors are perpendicular to each other. Final Answer: (B)
The component of vector $\vec{A}$ in the direction of $\vec{B}$ is given by $A \cos \theta$, where $\theta$ is the angle between them.
Step 2: Meaning
If the component is zero, then $A \cos \theta = 0$. Since the magnitude $A$ is non-zero, $\cos \theta$ must be zero.
Step 3: Analysis
The cosine of an angle is zero when the angle $\theta = 90^{\circ}$.
Step 4: Conclusion
An angle of $90^{\circ}$ means that the two vectors are perpendicular to each other. Final Answer: (B)
Was this answer helpful?
0
0
Top AP ECET Metallurgical Eng Physics Questions
- If the unit of mass is $1\text{ kg}$, the unit of length is $1\text{ m}$ and the unit of time is $1\text{ minute}$, the unit of pressure in $\text{Nm}^{-2}$ is
- $MLT^{-1}$ is the dimensional formula for
- If $|\vec{A} \times \vec{B}| = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $|\vec{A} + \vec{B}|$ is
- Of the vectors given below, the parallel vectors are $\vec{A} = 6\hat{i} + 8\hat{j}$, $\vec{B} = 210\hat{i} + 280\hat{k}$, $\vec{C} = 5.1\hat{i} + 6.8\hat{j}$, $\vec{D} = 3.6\hat{i} + 8\hat{j} + 48\hat{k}$
- The position $x$ of a particle with respect to time '$t$' along x- axis is given by $x = 9t^2 - t^3$ where $x$ is in metres and $t$ in seconds. The position of this particle when it achieves maximum speed along the x direction is
View More Questions
Top AP ECET Metallurgical Eng Mechanics Questions
- If $|\vec{A} \times \vec{B}| = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $|\vec{A} + \vec{B}|$ is
- Of the vectors given below, the parallel vectors are $\vec{A} = 6\hat{i} + 8\hat{j}$, $\vec{B} = 210\hat{i} + 280\hat{k}$, $\vec{C} = 5.1\hat{i} + 6.8\hat{j}$, $\vec{D} = 3.6\hat{i} + 8\hat{j} + 48\hat{k}$
- The position $x$ of a particle with respect to time '$t$' along x- axis is given by $x = 9t^2 - t^3$ where $x$ is in metres and $t$ in seconds. The position of this particle when it achieves maximum speed along the x direction is
- A ball is projected vertically up with a velocity of $40 \text{ ms}^{-1}$ from ground. At the same time another ball is dropped from a height of $100 \text{ m}$. The magnitudes of their velocities are equal after
- Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $\pi/8$ and the maximum height reached by it is $102$ metres. Then the maximum height reached by the other in metres is
View More Questions
Top AP ECET Metallurgical Eng Questions
- Order of the matrix $\begin{bmatrix} 1 & 6 \\ 2 & 0 \\ 7 & -1 \end{bmatrix}$ is
- If two rows (or columns) of a determinant of order 3 are identical then the value of determinant is
- Co-factor of -4 in $\begin{vmatrix} 1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9 \end{vmatrix}$ is
- The Matrix $\begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$ is
- If $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ then $(A^{-1}) =$
View More Questions