Vector Operations Dot Product Cross Product I Write the foll

Vector Operations (Dot Product Cross Product):

I. Write the following vectors in i, j, k, notation: ( the definitions for the following vectors will be used in Parts II and III)

a=(4, 0, 0) b=(2, 0.5, 0) c=(0, -3, 0)

d=(0, 0, 6) e=(-2, -8, 4) f=(3.5, 2, 7)

II. Compute the following dot products:

a·b a·c c·c

d·e e·d f·a

III. Compute the following cross products:

axb axc axa

dxe exf fxe

I) a = 4 i^ + 0 j^ + 0 k^

b = 2 i^ + 0.5 j^ + 0 k^

c = 0 i^ - 3 j^ + 0 k^

d = 0 i^ + 0 j^ + 6 k^

e = -2 i^ - 8 j^ + 4 k^

f = 3.5 i^ + 2 j^ + 7 k^

II) a.b = (4 i^ + 0 j^ + 0 k^).(2 i^ + 0.5 j^ + 0 k^) = (8 + 0 + 0) = 8

a.c = (4 i^ + 0 j^ + 0 k^).(0 i^ - 3 j^ + 0 k^) = (0 + 0 + 0) = 0

c.c = (0 i^ - 3 j^ + 0 k^).(0 i^ - 3 j^ + 0 k^) = (0 + 9 +0) = 9

d.e = (0 i^ + 0 j^ + 6 k^).(-2 i^ - 8 j^ + 4 k^) = (0 + 0 + 24) = 24

e.d = (-2 i^ - 8 j^ + 4 k^).(0 i^ + 0 j^ + 6 k^) = (0 + 0 +24) = 24

f.a = (3.5 i^ + 2 j^ + 7 k^).(4 i^ + 0 j^ + 0 k^) = (14 + 0 + 0) = 14

III) a x b = (4 i^ + 0 j^ + 0 k^) x (2 i^ + 0.5 j^ + 0 k^) = 2 k^

a x c = (4 i^ + 0 j^ + 0 k^) x (0 i^ - 3 j^ + 0 k^) = -12 k^

a x a = 0

a x e = (4 i^ + 0 j^ + 0 k^) x (-2 i^ - 8 j^ + 4 k^) = (-16 j^ - 32 k^)

e x f = (-2 i^ - 8 j^ + 4 k^) x (3.5 i^ + 2 j^ + 7 k^) = (-56-8) i^ + (14+14) j^ + (-4+28) k^ =(-64) i^ + (28) j^ +(24)k^

f x e = (3.5 i^ + 2 j^ + 7 k^) x (-2 i^ - 8 j^ + 4 k^) = (8+56) i^ + (-14-14) j^ + (4-28) k^ =(64) i^ + (-28) j^ +(-24)k^