exam1b

# exam1b - Name Math5B-F08 Midterm I B Work in the space...

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Name Math5B-F08 Midterm I B Work in the space provided (you may use the back). No books, notes, or calculators. 5 problems on 5 pages, 95 points, 5 bonus points for clean and neat work. Always show work and/or reasoning. Circle your ﬁnal answer! Problem 1 (25 pts: 11,6,8) (a) The points (0 , 0 , 0) , (1 , - 1 , 0), and (2 , 2 , 1), form the vertices of a space triangle. Find its area. (b) The vector ~ F = b i i b - 3 b j j + 2 b k b k represents a force; what is its scalar component (=scalar projection) in the direction of 4 b i b i i + 3 b k b k b k? (c) An origin vector in the ﬁrst octant makes the same angle with each of the three coordinate axes. What is the angle? [Write it in the form cos - 1 ( α ).]

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Problem 2 (21 pts: 10,7,4) Consider the plane P : 2 x - y - 3 z = 14. (a) Find the point P 0 where a line passing through P 1 : (1 , 2 , 0) and perpendicular to P intersects P . (b)
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exam1b - Name Math5B-F08 Midterm I B Work in the space...

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