Question

If p=3i-4j, then what is the perpendicular vector p?

Answer 1

Answer:

the dot product must be 0

let the perpendicular force be p = xi+yj

(xi+yj).(4i-3j)=0

4x-3y=0

x=3/4y

p=3/4i+j or p=3i+4j

Step-by-step explanation:

Answer 2

Answer:

$4 \hat{i}+3 \hat{j}$  is the perpendicular vector p.

Step-by-step explanation:

Given:

$\overrightarrow{\mathrm{P}}=3 \hat{i}-4 \hat{j}$

For perpendicular vector, dot product = 0.

For a vector $(a \hat{i}+b \hat{j}) is perpendicular to$ $(b \hat{i}-a \hat{j})$.

$(3 \hat{i}-4 \hat{j})\cdot(a \hat{i}+b \hat{j})=0$.

So, dot product of $\overrightarrow{\mathrm{P}} \& 4 \hat{i}+3 \hat{j}$ is equal to zero

$\begin{aligned}\overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{A}} &=(3 \hat{i}-4 \hat{j}) \cdot(4 \hat{i}+3 \hat{j}) \\&=12-12 \\&=0\end{aligned}$