Question

23. Given three unit vectors ā, b, cno two of which are collinear satisfying a
$a \times( b \times c) = b \div 2$
The angle between
a and b is
​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The angle between a and b satisfying the condition a×(b×c)=b÷2 is 90°

• Given,
• a,b and c are the collinear vectors.
• satisfying a condition a×(b×c)=b÷2
• Now,
• from given, we have,
• a×(b×c)=b÷2
• using vector properties, we have,
• ⇒(a.c)b-(a.b)c=$\frac{1}{2}.$b
• ⇒(a.c)b-$\frac{1}{2}.$b=(a.b)c
• ⇒(a.c-$\frac{1}{2}$)b=(a.b)c
• Since, given, the vectors are collinear,
• the possibilities are,
• a.c=$\frac{1}{2}$.a and
• a.b=0
• using scalar product of vectors, we get,
• a.b=0
• ⇒ angle between a and b is 90°