MATH 215 Midterm: exam1w05sol
Document Summary
First exam solutions (3x5= 15 points) this problem consists of three unrelated questions on vector algebra. Problem 1. and geometry. (a) two vectors ~v and ~w are of the form ~v = a( ~ + ~ ), and ~w = b~ + ~ , where a and b are scalars. If ~v + ~w + 10~ ~ = ~0, nd the scalars a and b. The vector equation is which is to say h0, 0i = h a + b + 10, ai. h0, 0i = h a, ai + hb, 1i + h10, 0i + h0, 1i, Answer: (a)a = 0, b = 10 (b) a constant force ~f = h 1 , 2 , 5i acts on a particle as it moves from a(2, 4, 1) to b( 2, 1, 3). ~f ~ab = h 1 , 2 , 5i h 4 , 3 , 2i = 4 6 10.
