Physics - Vectors Question with Solution | TestHub

Two vectors are normal to each other if their dot product is zero.

Given force vector $\vec{F}=4\hat{i}-3\hat{j}$.

Checking the dot product of $\vec{F}$ with each of the given vectors:

For option (1): $(4\hat{i}-3\hat{j})\cdot (-6\hat{i})=(4)(-6)+(-3)(0)=-24\ne 0$

For option (2): $(4\hat{i}-3\hat{j})\cdot (7\hat{i})=(4)(7)+(-3)(0)=28\ne 0$

For option (3): $(4\hat{i}-3\hat{j})\cdot (3\hat{i}+4\hat{j})=(4)(3)+(-3)(4)=12-12=0$

For option (4): $(4\hat{i}-3\hat{j})\cdot (4\hat{i}+3\hat{j})=(4)(4)+(-3)(3)=16-9=7\ne 0$

Since the dot product is zero for the vector $3\hat{i}+4\hat{j}$, it is normal to the given force vector.