Question: Show that the plane 2x - y - 3z = 4 is parallel to the line x = 2 + 2t, y = -1 +

Show that the plane 2x - y - 3z = 4 is parallel to the line x = −2 + 2t, y = -1 + 4t, z = 4, and find the distance between them.

Step by Step Solution

★★★★★

3.37 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The normal to the plane n 2 1 3 is perpendicular to the d... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 10th Edition Questions!

Q:

The ratio in which the plane r.(i-2 j+3k) = 17 divides the line joining the points -2i+4j+7k and si-5j+8k 1) 1:5 2) 1: 10 3) 3:5 4) 3: 10 If the points (1, 1, -3) and (1, 0, -3) lie on opposite sides...

Q:

By vector methods find the angle between the line x=y= 2z and the plane x+y+z=0. Find the angle between the plane x + y + z = 21 and the line x 1 = y + 2 = 2z +3. Find the equation of a line in the...

Q:

Find an equation of the plane perpendicular to D and through P, where D = 10i 10j + 5k and P is (1,1,-3). Find a plane crossing through (1,3,3), parallel to the plane 3x + y -z = 8. Is it possible to...

Q:

Please give me the answer~ 2. Find the equation of the line which passes through the point (1, 2, -3) and is perpendicular to the plane 2x + y + 3z = 4. Express your answer in the form r(t) = f (t) i...

Q:

10. Does the line through A(2,3, 2) and B(4, 0, 2) intersect the plane 2x + y - 3z +4 = 0? Explain

Q:

x+1 If q is the angle between the line :-2 and the plane 2x + y - 3z + 4 = 0 then 3 2 8 (cos ec*0) = 29 %3D

Q:

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

Q:

Harold Washington College Math 209 Practice Problems Test 1 Part 2 Name: Date: Solve the following problems. (1) Let ~ u, ~ v be vectors. Prove the identity ||~ u~ v||2 +|~ u~ v|2 = ||~ u||2||~ v||2....

Q:

1 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12 A. {(3 -...

Q:

Aaaaaaaaaa Show all work to receive any credit. Correct answers without supporting work will receive NO credit! 1. Consider the plane 2x + 2y - 32 = 18. (a) Find a point that is not on this plane....

Q:

Discuss the relative reliability of the different types of audit procedures.

Q:

According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less,...

Q:

1. Express each of the following expressions in the form (x + r) ^ 2 + u (a) x ^ 2 + 14x + 5 (b) x ^ 2 + 7x - 1.2 (c) x ^ 2 - 9x + 3 (d) x ^ 2 - 6/5 * x - 4

Q:

Managing successful organizational change is generally considered the most difficult of all competencies. Managing organizational change encompasses and coordinates numerous competencies. What...

Q:

Use Newtons method to approximate all the intersection points of the following pairs of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. y = 1/x and y =...

Q:

Evaluate the following limits using lHpitals Rule In x 1 lim >

Q:

A man wishes to get from an initial point on the shore of a circular lake with radius 1 mi to a point on the shore directly opposite (on the other end of the diameter). He plans to swim from the...

Q:

Consider a U.S.-based company that exports goods to Switzerland. The U.S. Company expects to receive payment on a shipment of goods in three months. Because the payment will be in Swiss francs, the...

Q:

The manager for a growing firm is considering the launch of a new product. If the product goes directly to market, there is a 40 percent chance of success. For $174,000 the manager can conduct a...

Q:

You have just been offered a job. Your base salary will be $90,000 per year and the first years annual salary will be received one year from the day you start working. You receive a bonus immediately...