Question

The line `(x - 2)/3 = (y - 3)/4 = (z - 4)/5` is parallel to the plane

Options

• 2x + 3y + 4z = 0

• 3x + 4y – 5z = 7

• 2x + y – 2z = 0

• x – y + z = 2

Answer 1

3x + 4y – 5z = 7

Explanation:

3x + 4y – 5z = 7

or 3x + 4y – 5z – 7 = 0

or `vecx = 3hati + 4hatj - 5hatk`

And `(x - 2)/3 = (y - 3)/4`

= `(z - 4)/5`

`vecb = 3hati + 4hatj + 5hatk`

`vecx.vecb = (3hati + 4hatj - 5hatk).(3hati + 4hatj + 5hatk)`

= 9 + 16 – 25

= 25 – 25

= 0