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:

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

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