Question

The vector a+3b is perpendicular to 7a-5b and a-4b is perpendicular to 7a-2b the angle between a and b is:

Answer 1

HELLO DEAR,

GIVEN:-

• (a + 3b) perpendicular to (7a - 5b)
• (a - 4b) perpendicular to (7a - 2b)

we know:- |a|² = |b|² = 1

now,

(a + 3b) perpendicular to (7a - 5b)

(a + 3b) . (7a - 5b) = 0

=> 7|a|² - 5|a.b| + 21|b.a| - 15|b|² = 0

=> 7a² + 16|a.b| - 15b² = 0

=> 7 - 15 + 16cos∅ = 0

=> ∅ = cos-¹(1/2)

=> ∅ = π/3

and,

(a - 4b) perpendicular to (7a - 2b)

(a - 4b) . (7a - 2b) = 0

=> 7|a|² - 2|a.b| - 28|b.a| + 8|b|² = 0

=> 7|a|² - 30|a.b| + 8|b|² = 0

=> 7 + 8 - 30cos∅ = 0

=> ∅ = cos-¹(1/2)

=> ∅ = π/3

therefore, the between a and b is π/3.

I HOPE IT'S HELP YOU DEAR,

THANKS