1) a straight line is given by the path vector R(t) = (1+t)i hat + (3t) j hat +

ID: 3287111 • Letter: 1

Question

1) a straight line is given by the path vector R(t) = (1+t)i hat + (3t) j hat + (1-t) k hat

a. find a non-zero vector parallel to this line

b. for what value of c and d will this line be perpendicular to the plane x+cy+dz=0?

c. find ds/dt (speed) for a point moving on this line.

2) An isoscelese triangle in plane M has sides of length a, a and b. Projecting onto plane M' forms

an equilateral triangle with sides b. If the angle theta is 30 degrees (pi/6), find a.

3) a. simplify "A hat * derivative of A hat"

b. simplify "vector A * ((vector B x vector A) x vector A)

c. find a vector that bisects the angle between vector A= 4 i hat + 3 j hat, vector B = i hat + 2 j hat (hint: use unit vector)

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