Let a b c be three vectors having magnitude 1,1 and 2 respectively If ax(axc)+b=0,then acute angle between a - Maths - Introduction to Three Dimensional Geometry

Question

Let a b c be three vectors having magnitude 1,1 and 2 respectively
If ax(axc)+b=0,then acute angle between a and c is

Mugdha Sharma · Answer

askiitians com 0 Home » Forum » Vectors » Let a,
b and c be three vectors with Let a, b and c be three vectors with
magnitudes 1, 1 and 2 respectively If ax(axc) + b = 0, then the
acute angle between a and c is? 11 months ago Answers : (1) Given
|a|= 1, |b|= 1, |c|= 2 Now a x( a x c) + b = 0 (a c)a - (a a) c =
-b (1 2 cos@) - c = - b 2 cos@ a = c -b (1) 2 cos@ a a = (c-b)a 2
cos @ = c a - b a 2 cos@ = 1 2 cos@ - a b Hence a b = 0 Again from
(1) 2 cos@ a b = (c-b) b = c b - b b 0 = c b -1 b c = 1 (2) Now
squaring (1) 4 cos²@ a² = c² + b² - 2b c 4
cos²@ = 4 +1 - 2 Cos² @ = ¾ Cos @ = large
sqrt3/2 Hence @ = large pi/6

Let a b c be three vectors having magnitude 1,1 and 2 respectively. If ax(axc)+b=0,then acute angle between a and c is