# HW21 - HW 21 Algebra II Honors Mr Petach Please write your...

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HW 21 Algebra II Honors – Mr. Petach Please write your answers on a separate sheet! 1. For each of the lines, i) ﬁnd a positively directed normal vector, ii) ﬁnd the positive unit normal vector, iii) ﬁnd the perpendicular distance from the origin to the line. (a) 3 y + 2 x - 6 = 0 (b) y = - 3 x + 4 2. Find the perpendicular distance from the point to the line (a) y = 1 2 x - 3 and (3 , 4) (b) 5 x - y + 2 = 0 and ( - 1 , 2) 3. Find the angle between the lines. Draw a picture! (a) 3 x + y = 4 and y = - x - 1 (b) ~ r ( t ) = 3 ~ i - j + t ( ~ i - ~ j ) and x - y = 0 4. For each of the planes, i) ﬁnd a positive normal vector, ii) ﬁnd the positive unit normal vector, iii) ﬁnd the perpendicular distance from the origin to the plane. (a) 20 x - 5 y - 4 z + 63 = 0 (b) 13 x + 16 = 0 5. Find the angle between a line connecting (1 , 1 , 2) and (2 , 4 , 3) and the normal vector to the plane x + y + 2 z - 4 = 0 6. A ship is moving south-southwest at 5 km/hr along a path given by ~ r ( t ) = ~ i + 6 ~ j + t

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## This note was uploaded on 05/13/2011 for the course MATH 101 taught by Professor Impemba during the Fall '10 term at Grand Valley State.

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HW21 - HW 21 Algebra II Honors Mr Petach Please write your...

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