Question

Vectors a = (3, 4) and b = (m, 2) are given. For which value of m they are perpendicular?

Answer 1

Answer:

The value of m is $-\frac83$.

Step-by-step explanation:

If two vectors $\vec A$ and $\vec B$ are perpendicular to each other then their dot product will be zero i.e $\vec A.\vec B=0$

If two vectors $\vec A$ and $\vec B$ are parallel to each other then their cross product will be zero i.e $\vec A\times\vec B=\vec 0$

Given vectors are a= (3,4) and b=(m,2)

The position vector of $\vec a$  is =$3 \hat i+4\hat j$

The position vector of $\vec b$  is =$m \hat i+2\hat j$

Since $\vec a$ and $\vec b$ are perpendicular.

Then,

$\vec a. \vec b=0$

$\Rightarrow (3\hat i+4\hat j).(m\hat i+2 \hat j)=0$

⇒3.m +4.2=0

⇒3m+8=0

⇒3m= -8

$\Rightarrow m=-\frac 83$

The value of m is $-\frac83$.