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September 20, 2014

September 20, 2014

Posted by **Roberto & Cecilia** on Thursday, June 21, 2012 at 4:01pm.

QUESTION:

Write a vector equation and parametric equations for a plane that satisfies each set of conditions.

a) contains the point P̥(2,-4,6); has direction vectors a = [6,-7,0] and b = [4,1,3]

b) contains the point P̥(-5,9,-3); is parallel to the lines [x,y,z] = [1,-2,7] + s[4,-1,-3] and [x,y,z] = [7,-2,15] + t[1,6,-8]

c) contains the points A(4,-2,5), B(3,-3,1), and C(5,2,8)

d) has x-intercept 12, y-intercept -4, and z-intercept 7

please and thank you!

- CALCULUS EXAM REVIEW -
**Reiny**, Thursday, June 21, 2012 at 5:05pmTo write the vector equation of a plane you need two different direction vectors on the plane, and a point on the plane

a) you are given exactly what I described above

so

r = (2,-4,6) + s(6,-7,0) + t(4,1,3)

It is easy to write these in parametric form

x = 2 + 6s + 4t

y = -4 -7t

z = 6 = 3t , it should be obvious what I did.

b) each of the lines gives you a direction vector, and you are given a point, so ....... (same question)

c) You can find vector AB and vector AC or vector BC , and you have the choice of 3 different points,

d) "has x-intercept 12, y-intercept -4, and z-intercept 7" translates to ...

you are given the points (12,0,0), (0,-4,0) and (0.0.7). Now it becomes the same kind of problem as c)

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