Question

Let a=2i+3j+4k and b=3i+4j+5k. Find the angle between them.

Answer 1

Thanks for asking the question!

ANSWER::

Given :-
a=2i+3j+4k
 b=3i+4j+5k

Magnitude of a vector =√(2²+3²+4²) =√29
Magnitude of b vector =√(3²+4²+5²) =√50 

Dot product of these vectors , a.b = abcosФ 
Ф = cos⁻¹ (a .b) / (ab)
Ф = cos⁻¹ (2x3 +3x4 + 4x5)/(√(2²+3²+4²)√(3²+4²+5²)) = cos⁻¹(38/√1450)

So , the angle between them is cos⁻¹(38/√1450)

Hope it helps!