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Mathematics
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Cambridge University
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Homework
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1 1 (b) 2 x = (2, 1, 3) + s(1. − 1, 2) is the equation os straight line. x = (1, 2, −1) + s(1, 1, −2) + t(2, 2, −4) is also a line, which can be seen by defining a new parameter r = s + 2t. In this way, we may rewrite the equation as x = (1, 2, −1) + r(1, 1, −2). All other equations have more than one parameter, so define surfaces. 2 The normal vectors are, respectively n# 1 = (1, 2, −2) and n# 2 = (2, −1, −2). The angle between the planes is the angle between the normal vectors. Calling this angle θ, cosθ = 2−2+4 4 n# 1 · n# 2 √ =√ = . # kn1 kkn# 2 k 9 1+4+4 ...
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