Question

find A .B and the angle between the vectors: A= i^- 2 j^ - 5 k^ and
B=2i^+j^ - 4K^
​

Answer 1

Explanation:

Magnitude of:

A = √1² + 2² + 5² = √30

B = √2² + 1² + 4² = √21

 Let the angle between them be O.

A.B = ABcosO = √30 * √21 * cosO

  Also,

A.B = (i - 2j - 5k)(2i + j - 4k)

      = 2(1) - 2(1) + 20(1)

      = 20

Hence,

⇒ 20 = √30 * √21 cosO

⇒ 20 = $\sqrt{3*10}*\sqrt{3*7}$cosO

⇒ 20 = 3√70 cosO

⇒ $\frac{20}{3\sqrt{70}}=cosO$

⇒ $cos^{-1}\big(\frac{20}{3\sqrt{70}}\big)=O$