Question

The vector equation of the plane passing through point `A(bara)` and parallel to `barb` and `barc` is ______.

Options

• `(barr - bara) xx (barb xx barc) = bar0`

• `(barr - bara) · (barb + barc) = 0`

• `(barr - bara) · (barb xx barc) = 0`

• `(barr - bara) xx (barb - barc) = bar0`

Answer 1

The vector equation of the plane passing through point `A(bara)` and parallel to `barb` and `barc` is `bbunderline((barr - bara) · (barb xx barc) = 0)`.

Explanation:

As vectors `barb` and `barc` are parallel to the plane, vector `barb xx barc` is normal to the plane. Plane passes through `A(bara)`.

Let `P(barr)` be any point on the plane.

∴ `bar(AP)` is perpendicular to `barb xx barc`.

∴ `bar(AP) · (barb xx barc) = 0`

∴ `(barr - bara) · (barb xx barc) = 0`