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## Homework Statement

The planes ∏1 and ∏2 have equations 3x - y - z = 2 and x + 5y + z = 14 respectively. Show that the point (3,1,6) lies on both planes.

The Question:

By finding the coordinates of another point lying in both planes, or otherwise, show that the line of intersection of ∏1 and ∏2 has equation r = 3

**i**+

**j**+ 6

**k**+ t (

**i**-

**j**+ 4

**k**).

## Homework Equations

Show point (3,1,6) lies in both planes:

Substitute point (3,1,6) into the

**r**of both plane equations.

## The Attempt at a Solution

The first part:

Let point (3,1,6) be

**a**

Substitute

**a**into

**r**of both plane equations.

The dot product of

**a**and

**r**= ''d" of the plane equations.

LHS=RHS [Shown]

How do I attempt the second part of the question? I do not quite understand the second part of the question.

Please help me. :uhh:

Thanks!