# Calculus

Consider the planes given by the equations
2y−2x−z=2
x−2y+3z=7
(a) Find a vector v parallel to the line of intersection of the planes.

(b)Find the equation of a plane through the origin which is perpendicular to the line of intersection of these two planes.

For part a) I just used the cross product of the vectors and got -8i-7j-2k
Then for part b) I used the vector I got for part a) and the point (0,0,0) to get -8x-7y-2z=0

Both answers are wrong and I don't know why.

1. 👍 0
2. 👎 0
3. 👁 476
1. Your method is correct, except you must have made an arithmetic error,
I got (-4, -5, -2) as the cross-product

a) which we can change to (4,5,2)
b) since we have a point (0,0,0)
the equation of the required plane is
4x + 5y + 2z = 0

Another way:

Add the two equations
-x + 2z = 9
x = 2z-9

let z = 0, ----> x = -9
sub into 2nd equation, y = -8

let z = 4, ---> x = -1
sub into 2nd equation, y = 2
So we have 2 points on the line of intersection,
(-9, -8, 0) and (-1, 2,4)
and a direction vector would be
(8, 10, 4)
or reduced to (4,5,2) as above

1. 👍 0
2. 👎 1

## Similar Questions

1. ### Calculus

Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z = 5 a) Find parametric equations for the line of intersection of the planes. b) Find the angle between the planes

2. ### Physics

You are given vectors A = 5.0i - 6.5j and B = -2.5i + 7.0j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 15.0. Find the x and y components to vector C. Here's

3. ### math calculus 3

find a formula for a function g( x,y,z) whose level surfaces are planes parallel to z=3x-2y+7

4. ### Physics

If vector A=2i+3j-k and B=4i+2j-2k find vector x parallel to A but has magnitude of B

1. ### Calculus

Find the distance between the given parallel planes. 5x−4y+z=10, 10x−8y+2z=3

2. ### Calculus

Find the distance between the given parallel planes. 4z = 4y − 4x, 6z = 3 − 6x + 6y

3. ### Physics

Find the unit vector parallel to the vector : C=12i+24j-8k. A.9/7i+5/7j+1/7k B.3/7i+6/7j-2/7k. I think B is correct. Please tell me correct option and method of finding.

4. ### Calculus II

find the distance between the given parallel planes 5x-5y+z=10 and 10x-10y+2z=2. I got 9sqrt51/51

1. ### jane

1. a centripetal-acceleration addict rides in uniform circular motion with period T=2s and radius r=3m. at t1 his acceleration vector= 6(m/s^2)i + -4(m/s^2)j. At that instant, what are the values of vector b (dot) vector a and

2. ### Calculus

Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4

3. ### Math

1. Determine the scalar equation of the plane with vector equation Vector r= (3,-1,4) +s(2,-1,5) + t(-3,2,-2). 2. Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = kt is parallel to

4. ### math

1. A skateboard ramp has a 158º entry angle. Find the measure of ∠1. A.) 22º B.) 68º C.) 78º D.) 58º 2. Which of the following equations parallel to the line passing through A(-2, 7);B(-2, -2)? A.) y = -2 B.) y = x C.) 3x =