Question

If the vectors `xhat"i" - 3hat"j" + 7hat"k" and hat"i" + "y"hat"j" - "z"hat"k"` are collinear then the value of `"xy"^2/"z"` is equal.

Options

• `9/7`

• `(- 9)/7`

• `(- 7)/9`

• `7/9`

Answer 1

`(- 9)/7`

Explanation:

Given, vectors `xhat"i" - 3hat"j" + 7hat"k" and hat"i" + "y"hat"j" - "z"hat"k"` are collinear

∴ `x/1 = (-3)/"y" = 7/(- "z")`= k

⇒ x = k, -3 = ky and 7 = - kz

Now, `"xy"^2/"z" = ("k"(- 3/"k")^2)/((- 7)/"k")`

`= (9/"k")/((- 7)/"k")`

`= (- 9)/7`