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MATH 2D Midterm: MATH2D Midterm 1 2013 Winter

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turquoisegnu128

15 Oct 2018

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$MATH 2D Full Course Notes$

MATH 2D Full Course Notes

Document Summary

Determine whether the given vectors are orthogonal, parallel, or neither: < 1, 2, 3 > and < 3, 0, 1 > V =< 1, 2, 3 >, u =< 2, 0, 1 >, w =< 2, 1, 1 : 2 v + 2 u w, | v u, v ( u w) Find the equation of the plane through (1, 2, 3) that contains the line x = t + 2, y = 2t 3, z = t + 1. Answer: 9x y + 7z = 28. Find the distance from the origin to the line x = 2t + 2, y = t 3, z = t 4 (cid:113) 55. Reduce the equation to one of the standard forms, classify the surface: x2 + 2y2 + 3z2 2x 4y 6z 15 = 0. Answer: (x 1)2 a2 + (y 1)2 b2 + (z 1)2 c2 = 1, where a2 = 21, b2 = 21/2, c2 = 7.

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Related Questions

Question1.

a)

Let L be the line containing thepoint P(2,-5,-1) and perpendicular to theplane 2x1+3x2+2x3=-3.

Find a vector equationfor L.

My answer: <2,-5,-1>+ t<2,3,2> (correct)

b)

At what pointdoes

Lintersect the yz-plane?

Question2:

x1 = -6 t - 4

x2 = - t+ 2

x3 = 5t - 6

and the second set ofparametric equations

x1 = 6t

x2 = ?

x3 = ?

describe the same line inR3. Find x2 and x3.

Question3:

It is one of 3 options foreach one: Parallel, perpindicular, or neither. Please explainwhy.

http://imgur.com/UbDuH8Z

Question4:

Find the point ofintersection of the two lines

a)

L1: x=1+t, y=-10-2t, z=-5-2t,

L2: x=7-4s, y=-10+2s, z=-7+3s.

Note that in general, twolines in 3D do not intersect. These two lines are carefully chosenso that they do

b)

Find the point where theline

x=1+2t,y=-4+t,z=-2-2t

intersects theplane

4x-y+3z=3.

Thanks. I have a lot ofpoints for this and will give it to someone that can helpme.

(a) Find a vector w with magnitude 20 that is parallel to v =<3, 4, 2>

b.) give the angle between vectors a=3i-j+5k and b=i+2j (Give anexact expression for your answer and then approximate to thenearest degree.)

c.)Let P be the point with polar coordinates (3,2pi/3). Give apolar coordinate representation (r,?)for P with -pi/2<=?<=pi/2

d.) Consider the quadratic surface represented by the equation x^2- 81y^2 + z^2 = 0

i. Identify the trace of the surface in the plane y = 1.(i.e., Is it an ellipse, a circle, a

parabola, a hyperbola, etc?)

ii. Identify the trace of the surface in the plane x = 1.(i.e., Is it an ellipse, a circle, a

parabola, a hyperbola, etc?)

iii. Identify the surface. (i.e., Is this an ellipsoid,paraboloid, cone, hyperboloid of one

question 23 please