Question

a=2i+2j-k
b=6i-3j+2k​

Answer 1

Step-by-step explanation:

A=2 i + 2 j - 1 k and B = 6 i - 3 j + 2 k (Bold denotes vectors and i, j, and k are unit vectors in the x, y and z directions, respectively). Then the dot (scalar) product is;

A . B = |A| |B| cos(theta) and A . B = 2 x 6 -2 x 3 - 1 x 2 = 4 , |A| = 3 and |B| = 7

and we get 4 = 3 x 7 cos(theta). Solving, cos(theta) = 4/21 = 0.19

Finally, theta = 79 degrees.

Answer 2

Answer:

Letθ be the angle between to vectors and

a⃗ =2i+2j−kandb⃗ =6i−3j+2k

a⃗ .b⃗ =|a⃗ |∣∣b⃗ ∣∣cosθ

a⃗ .b⃗ =2(6)+2(−3)+(−1)(2)=4

|a⃗ |=4+4+1−−−−−−−√=3

∣∣b⃗ ∣∣=36+9+4−−−−−−−−√=7

cosθ=a⃗ .b⃗ |a⃗ |∣∣b⃗ ∣∣

cosθ=43×7=421

θ=cos−1421=79∘