Question

What is the midpoint of the vector joining the point P(2, 3, 4) and Q(4, 1, –2)?

Options

• `3hati + 2hatj + hatk`

• `2hatj + hatk`

• `3hati + hatj + hatk`

• `hatk - hati`

Answer 1

`3hati + 2hatj + hatk`

Explanation:

Midpoint of vector joining the points P`(veca)` and Q`(vecb)` is `(veca + vecb)/2`

Here, `veca = 2hatj + 3hatj + 4hatk, vecb = 4hati + hatj - 2hatk`

∴ Required mid point is = `((2hati + 3hatj + 4hatk) + (4hati + hatj - 2hatk))/2`

= `((2 + 4)hati + (3 + 1)hatj + (4 - 2)hatk)/2`

= `(6hati + 4hatj + 2hatk)/2`

= `3hati + 2hatj + hatk`