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Unformatted text preview: Math 178
Kouba
Discussion Sheet 11 1.) Find an equation in parametric fOrm of the line a.) in R2 passing through the point (2, —1) and parallel to the vector < . b.) in R2 passing through the point (3, 2) and perpendicular to the vector .
c.) in R2 passing through the points (4, 0) and (—1, 3) .
3
d.) in R3 passing through the point (0,2, 1) and parallel to the vector —1
2
e.) in R3 passing through the points (1, 2, 3) and (4, 5, 6) . 2.) Determine an equation for the plane passing through the point (—1, 0,4) and which is
2
perpendicular to the vector 1
—3
3.) Determine a point on the plane :c + 231 + 32 = 12 and a vector which is perpendicular
to it. 4.) Determine an equation of the plane which is parallel to the plane 3:5 —— 2y + z z 0 and
which passes through the point (1, ——1,0). 5.) Determine an equation of the plane which passes through the point (1, —1,0) and m=3+ﬁ
which is perpendicular to the line given parametrically by L : { y = ——1 — t .
z = 2 + t 6.) Determine an equation of the line in parametric form which passes through the point
(2, —3, 1) and which is perpendicular to the plane 3m — y + z = 5 . 7.) Find three points which lie on both of the planes :r — y + z = 1 and 2x + y — z = 3. 8.) Determine an equation Of the line in parametric form which represents the intersection
oftheplanesm—y+z=2and 3m+y—4z=1. 9.) Determine the point of intersection of the plane In — y + 22 = 4 and the line given a: = t
parametrically by L z { y ; 1 — t .
z = 1 + 2t 10.) The following lines intersect. Determine their point of intersection :
:1: = 1 + t a} = S
L:{y=2t and .M:{y=2+s
z = —1 + t z = —2 + s l 3 12.) Determine the angle 9 between the vector 2 1 11.) Determine the angle 0 between the vectors (—4 and —2 0 3 2 and the line given parametrically by
1 12:32?
L:{y=1+t
z=1—2t 13.) Determine the angle 0 between the planes 2 2 2:1: — y and :1: + 2y + 32 = 6. 14.) Find the point of intersection of the plane 310  2y + z = 24 and the line passing
through the point (2, —1, 3) which meets the plane orthogonally. “ ..., because this is America.”— Kouba ...
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 Winter '07
 Kouba

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