Question

P = î +2j +3k and Q=2i-j-k
find the angle between (2P + Q) and (P + 2Q).​

Answer 1

Answer:

60 degree

Explanation:

Sol : 2P+Q = 2(i+2j+3k) + 2i-j-k = 4i+3j+5k

and P-2Q = i+2j+3k - (4i-2j-2k) = -3i+4j+5k

Now angle b/w them is given by using : cos(theta) = a.b/|a|×|b| ,where a and b are two vectors and theta is the angle b/w them.

So,

cos(theta) = [(4i+3j+5k).(-3i+4j+5k)]/(√50×√50)

where √50 is magnitude of both required vectors.

So, cos(theta) = 25/50 = 1/2

or theta = cos^-1(1/2) = π/3 or 60°

So angle b/w required vectors is 60° or π/3