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

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(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 $\vec{F}$?

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