Disc11 - Math 178 Kouba Discussion Sheet 11 1.) Find an...

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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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This note was uploaded on 02/17/2012 for the course MATH 17B taught by Professor Kouba during the Winter '07 term at UC Davis.

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Disc11 - Math 178 Kouba Discussion Sheet 11 1.) Find an...

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