Question

Find the equation of line which passes through the point (1, 2, 3) and is parallel to the vector `3hati + 2hatj - 2hatk`

Options

• `(hati + 2hatj + 3hatk)`

• `lambda(3hati + 2hatj - 2hatk)`

• `(3hati + 2hatj - 2hatk)`

• `(hati + 2hatj - 3hatk) + lambda(3hati + 2hatj - 2hatk)`

Answer 1

`(hati + 2hatj - 3hatk) + lambda(3hati + 2hatj - 2hatk)`

Explanation:

Equation of the line passing through the point `veca` and parallel to vector `vecb` is `vecr = veca + lambda vecb`

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

∴ Equation of the required line is `vecr = (hati + 2hatj + 3hatk) + lambda(3hati + 2hatj + 2hatk), lambda` ER