math20C_W07_Practice_mid1

# math20C_W07_Practice_mid1 - a b is orthogonal to a . 3 3....

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Math 20C, Practice Midterm 1 January 23, 2007 Name: Section: This exam consists of 7 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justiﬁcation will receive no credit. 3. You may use one 4-by-6 index card, both sides. 4. You are not allowed to leave your seat if the remaining time is less than 5 minutes. Score 1 10 2 10 3 10 4 10 5 10 6 10 Total 60 1

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1. (a) Find the center and radius of the sphere give by the equation x 2 + y 2 + z 2 - 2 y = 0 (b) Find the number a so that the two vectors a = h 1 ,a, 2 i and b = h- 5 , 3 ,a i are orthogonal to each other. 2
2. Let a and b are 3 dimensional vectors. Show that

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Unformatted text preview: a b is orthogonal to a . 3 3. Find a unit vector vector ( i.e. a vector with magnitude 1) which is orthogonal to both 2 i-j + k and i + j . 4 4. Find the equation of the plane that contains the points A (3 ,-1 , 2), B (8 , 2 , 4), and C (-1 ,-2 ,-3). 5 5. Let L be the line passing through the points A (1 , 2 , 3) and B (-1 , 1 , 1). Find the point at which L intersects the plane y-z = 0. 6 6. Find the equation of the line that passes through the origin and parallel to the line of intersection of the planes x + 2 y-z = 0 and y + z + 6 = 0. 7...
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## math20C_W07_Practice_mid1 - a b is orthogonal to a . 3 3....

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