For the vectors below, find a) A • B and b) the angle between A and B?

Question

A = (3i – 4j + 4k)

B = (2i + 3j – 7k)m

for a.) my answer is 34, since
(AxBx) + (AyBy) + (AzBz)
(3*2) + (-4*3) + (4*-7) = 34

i don't know how to solve b.)
should i use dot product or cross product to solve it?

Answer 1

　

(a) −34 is correct



(b) Use dot product



cosθ = A • B / (||A|| * ||B||)



||A|| = √(9+16+16) = √41

||B|| = √(4+9+49) = √62



cosθ = −34/√2542

θ = 132.4°

Answer 2

a • b = 6 - 12 - 28 = - 34

I a I = √ [ 9 + 16 + 16 ] = √ 41

I b I = √ [ 4 + 9 + 49 ] = √ 62

a • b = I a I I b I cos Ө

cos Ө = - 34 / [ √ 41 √ 62 ] = - 34 / 50.4

Ө = 132•4⁰ , 227•6⁰



Ө = 132 • 4 ⁰

Answer 3

A.B = |A| x |B| x cosΘ where Θ is the angle between them.

So Θ = arccos (A.B / (|A|x |B|))