Question

If vector a=(x,2,-6) and vector b=(1,-1,-6) and a=b find the value of x?

Answer 1

`x = sqrt(2)i`

Explanation:

The formula for the magnitude of a vector can be used to solve for `x`:

vector magnitude: `sqrt(x^{2}+y^{2}+z^{2})`

Since the magnitude of `vec{a}` is equal to the magnitude of `vec{b}`:
`a = b`
`sqrt(x^{2}+(2)^{2}+(-6)^{2}) = sqrt((1)^{2}+(-1)^{2}+(-6)^{2})`
`x^{2}+(2)^{2}+(-6)^{2} = (1)^{2}+(-1)^{2}+(-6)^{2}`
`x^{2}+4+36 = 1+1+36`
`x^{2}+40 = 38`
`x^{2} = -2`
`x = sqrt(-2)`
`x = sqrt(2)i`