Consider a vector vec{F} = 4 hat{i} - 3 hat{j | vedclass

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

Question

(D) Two vectors $\vec{A}$ and $\vec{B}$ are perpendicular if their dot product is zero,i.e.,$\vec{A} \cdot \vec{B} = 0$.Let $\vec{F} = 4 \hat{i} - 3 \

Vedclass · Accepted Answer

$3 \hat{i} + 4 \hat{j}$

Vedclass · Answer

(D) Two vectors $\vec{A}$ and $\vec{B}$ are perpendicular if their dot product is zero,i.e.,$\vec{A} \cdot \vec{B} = 0$.Let $\vec{F} = 4 \hat{i} - 3 \hat{j}$.Check the options:$(A)$ $(4 \hat{i} - 3 \hat{j}) \cdot (4 \hat{i} + 3 \hat{j}) = (4)(4) + (-3)(3) = 16 - 9 = 7 
eq 0$.$(B)$ $(4 \hat{i} - 3 \hat{j}) \cdot (6 \hat{i}) = (4)(6) + (-3)(0) = 24 
eq 0$.$(C)$ $(4 \hat{i} - 3 \hat{j}) \cdot (7 \hat{k}) = (4)(0) + (-3)(0) + (0)(7) = 0$. Since the dot product is $0$,this vector is perpendicular.$(D)$ $(4 \hat{i} - 3 \hat{j}) \cdot (3 \hat{i} + 4 \hat{j}) = (4)(3) + (-3)(4) = 12 - 12 = 0$. Since the dot product is $0$,this vector is also perpendicular.Note: Both $(C)$ and $(D)$ are perpendicular to $\vec{F}$. However,in standard multiple-choice contexts where only one answer is expected,$(D)$ is a common vector in the same plane,while $(C)$ is perpendicular to the plane. Given the options provided,$(D)$ is the most standard vector solution in the $xy$-plane.

Consider a vector $\vec{F} = 4 \hat{i} - 3 \hat{j}$. Which of the following vectors is perpendicular to $\vec{F}$?

Similar Questions

The angle between force $\vec{F}=3 \hat{i}+4 \hat{j}-5 \hat{k}$ and displacement $\vec{d}=5 \hat{i}+4 \hat{j}+3 \hat{k}$ is

If $F_1$ and $F_2$ are two vectors of equal magnitudes $F$ such that $|F_1 \cdot F_2| = |F_1 \times F_2|$,then $|F_1 + F_2|$ is equal to

Define the vector product of two vectors.

What will be the projection of vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ on vector $\vec{B} = \hat{i} + \hat{j}$?

Two unit vectors $\hat{a}_{1}$ and $\hat{a}_{2}$ are inclined to each other at an angle $\theta$. If $|\hat{a}_{1}-\hat{a}_{2}|=\sqrt{3}$,then the value of $(\hat{a}_{1}-\hat{a}_{2}) \cdot (2\hat{a}_{1}-\hat{a}_{2})$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module