MATH 21A Midterm: MATH 21A Harvard 21a Spring 09Midterm1 review problems
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Suppose that a and b are two vectors such that b is twice as long as a. If the angle between a and is 60 degrees, calculate the value of (a + 2b) (a b) 2 let r1(t) = ht, 2, 1i and r2(t) = ht, 1, 2i be two vector-valued functions, where t represents time in seconds. Consider the the parallelogram determined by by the vectors r1(t) and r2(t). 3 find the equation of a plane that passes through points p (5, 3, 2) and q(3, 1, 0) and that never intersects the y-axis. 4 consider two planes with normal vectors n1 = h20, 40, 0i and n2 = h0, 26, 26i, respectively. Suppose that both planes contain the point (1, 1, 1). Find a vector equation that parameterizes the line of intersection of these two planes. 5 a pitcher on the math 21a baseball team gets ready to pitch a baseball.
