QUESTION 1)

2. Consider the triangle in R3 with vertices A : (0, 2,4), B : (3, 3,4) and C : (1, 2, 3). Use vector projections to nd the point of intersection of the line L passing through B and C and the line that is perpendicular to L and that passes through A. 3. Suppose that the positions of two particles at the time t are given by r1(t) : 2 cos(t) sin2 (t)i + sin(t) j r2(t) : sin(t)i + cos(t)j Dene mg(t),y(t) by r4(t) : x(t)i + y1v(t)j for i E {1, 2}. (3.) Express the set X : {t E R : y1(t) : y2(t)} in abbreviated form. Note that X is innite. (b) Use your answer to (a) to nd the set C of tvalues for which there are collisions between the particles. (c) Find the two places in R2 at which the collisions you found in (b) occur. Let v = (3, 0, 1) and W = (5, 5, 1). Compute the following quantities: a. The parallel projection of v onto W b. The perpendicular projection of v onto W n= c. The unit vector i} a=