calculus cosine angle?

Question

the cosine of the angle between a and b is 4/21. Find P is a= 6i+3j-2k and b= -2i+pj-4k

Answer 1

Use the definition of the dot product.

Answer 2

A . B=A dot B= ab Cos (x) Where A,B are vectors and a,b are magnitudes of the vector

a=49, b=20+p^2

(-2*6)+(3p)+(2*4)=(49)(20+p^2)(4/21)

you have then quadratic eqaution of second degree
solve it you will have the values of P