Question

What will be the cartesian equation of the following plane. `vecr * (hati + hatj - hatk)` = 2

विकल्प

• `2x + 3y - 4x` = 1

• `x + y - z` = 2

• `x + 3y - z = 1/2`

• `x + 2y - 3z` = 1

Answer 1

`x + y - z` = 2

Explanation:

`vecr = xhati + yhatj + zhatk`

`vecr = (hati + hatj + hatk)` = 2

⇒ `(xhati + yhati + zhatk) * (hati + hatj - hatk)` = 2

⇒ `(x)(1) + (y)(1) + (z)(-1)` = 2

⇒ `x + y - z` = 2

Which is the required cartesian equation.