Given the vectors: v1 = 3m/s ˆi + 4m/s ˆj and v2 = 2m/s ˆi + 1m/s ˆj, calculate the following: (a) v1 + v2

(b) v1 − v2

(c) v2 − v1

(d) 3 ∗ v1 + 2 ∗ v2

(e) −4 ∗ v1 + 2 ∗ v2

(f) 0.5 ∗ v1 − 0.6 ∗ v2

Anyone please, thanks.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?