Question

JEE MAINS MATHS QUESTION SEPTEMBER 2020

Answer 1

If a, b, c are three vectors such that |a| = 2 , |b| = 2 and |c| = 4, b.c = 0 , b.a = c.a

To find : the value of |a + b - c |

solution : we know, from algebraic formula,

(x + y + z)² = x² + y² + z² + 2(xy + yz + yz)

so, (|a + b - c|)² = |a|² + |b|² + |c|² + 2(a.b - b.c - c.a)

given b.a = c.a and b.c = 0

so, (a.b - b.c - c.a) = 0

now (|a + b - c|)² = |a|² + |b|² + |c|² + 2 × 0

= |a|² + |b|² + |c|²

= 2² + 2² + 4²

= 4 + 4 + 16

= 24

so, |a + b - c | = √(24) = 2√6

Therefore the value of |a + b - c| is 2√6 so option (4) is correct.