Find the cosine of the angle between vectors a and b if a {-2; 1; -1}; b {1; 3; 2}

a (- 2; 1; – 1); b (1; 3; 2)

cos x = (a¯ * b¯) / (| a¯ | * | b¯ |),

a¯ * b¯ = – 2 * 1 + 1 * 3 + (- 1) * 2 = – 2 + 3 – 2 = – 1.

a¯ = √ ((- 2) 2 + 12 + (- 1) 2) = √ (4 + 1 + 1) = √6,

b¯ = √ (12 + 32 + 22) = √ (1 + 9 + 4) = √14,

cos x = (a¯ * b¯) / (| a¯ | * | b¯ |) = (- 1) / (| √6 | * | √14 |) = – 1 / (√84) =

– 1 / √ (4 * 21) = – 1 / 2√21.

The angle is between 96 ° – 97 °.

Answer: cos x = – 1 / 2√21. The angle is 96 ° – 97 °.