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Asked Nov 21, 2019
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2
r22
2.(a) Find the parametric and symmetric equation of a line passing through (-4, 1, 2) and
perpendicular to the plane x +2y + rz 3
X+2Yt2zz 3
(b) Find the point of this line with the y-z plane.
rz 2
3. Find the equation of the plane passing through A(-1, 2, 0), B(2, 0, 1) and C(r, 3, 1)
C (2,3,1)
4. Determine whether the lines given by the following symmetric equations are parallel,
perpendicular or skew:
ra d
y-2
3
Z-3
4
-1
2
+1
6
y-3
-1
-2
II II
II
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2 r22 2.(a) Find the parametric and symmetric equation of a line passing through (-4, 1, 2) and perpendicular to the plane x +2y + rz 3 X+2Yt2zz 3 (b) Find the point of this line with the y-z plane. rz 2 3. Find the equation of the plane passing through A(-1, 2, 0), B(2, 0, 1) and C(r, 3, 1) C (2,3,1) 4. Determine whether the lines given by the following symmetric equations are parallel, perpendicular or skew: ra d y-2 3 Z-3 4 -1 2 +1 6 y-3 -1 -2 II II II

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Expert Answer

Step 1

Hello. Since you have posted multiple questions and not specified which question needs to be solved, we will solve the first question for you. If you want any other specific question to be solved then please resubmit only that question or specify the question number.

 

(a) First of all, consider the point for which the parametric equation needs to be calculated. The point is (4, 1, 2).

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(x..yo. )= (4,1,2) and AxBxCx+ D = 0 So, x2y2=3 x+2y2: -3 0 A 1, B 2 and C = 2

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Step 2

Now, put the values and get the parametric equation to get the line passing through (4, 1, 2) perpendicular to the line x + 2y +2z = 3.

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y = y. + Bt +C x = 4 y 1+ 2 2+2

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Step 3

Now, to get the symmetric equation use the parametric equation....

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x 4 So, t x4 y-1 y 1+2 2 2 - 2+2 2 x-x y=y В С A х — 4 у- =t 2 2 х— 4 у-1 :-2 2 2 1

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