Show that the point (−1,−1,1) lies on both planes. Then find a vector parametric equation for the line of intersection.

YES , Point (-1, -1, 1) lies on plane

Step-by-step explanation:

Given:

Equation of plane;

-4x + 2y - z = 1

3x - 2y + 2z = 1

Prove:

Point (-1, -1, 1) lies on plane

Computation:

In equation 1

-4x + 2y - z = 1

By putting values

-4(-1) + 2(-1) - (1) = 1

4 - 2 - 1 = 1

1 = 1

So,

Point (-1, -1, 1) satisfy plane

In equation 2

3x - 2y + 2z = 1

By putting values

3x - 2y + 2z = 1

3(-1) - 2(-1) + 2(1)

-3 + 2 + 2 = 1

1 = 1

So,

Point (-1, -1, 1) satisfy plane

So,

Point (-1, -1, 1) lies on plane

Learn more:

the third picture

step-by-step explanation:

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116