Question

if vector ( a cap +2 b cap) is perpendicular. to vector (5a cap - 4b cap), then find the angle between a cap & bcap.​

Answer 1

Answer:

60°

Explanation:

since x • y = |x| |y| cos @

(a^ + 2b^) • (5a^- 4b^) =0 (cos90° =0)

5(a^•a^)-4(a^•b^) +10(a^•b^)-8(b^•b^) =0

5 - 8 + 6(a^•b^)= 0

(a^•b^) = 1/2

i.e, (a^•b^) = |a^| |b^| cos@

but |a^| = |b^| =1

hence (a^•b^) = 1/2 = cos 60°

therefore angle b/w a^ & b^ = 60°

Note:

1) |a^| = |b^| = 1

2) (a^ • a^) = |a| |a| cos 0° = 1

3) (b^ • b^) = |b| |b| cos 0° = 1