Question

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

Answer 1

The value of m is
`-\frac83`.

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*\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`.