Question

if three +vector A, b AND c ARE 12, 5 AND 13 IN MAGNITUDE SUCH THAT c=a+b then the angle between a and b is

Answer 1

Answer:

π/2

Explanation:

Given

a, b, and c are three positive vectors.

|a| = 12, |b| = 5 and |c| = 13

c = a + b

Squaring on both sides

⇒|c|² = |a + b|²

⇒|c|² = |a|² + |b|² + 2a.b  {∵ |p+q|² = |p|²+|q|²+2p.q where p.q is the dot

                                            product of the vectors p and q}

⇒13² = 12² + 5² + 2a.b

⇒169 = 144 + 25 + 2a.b

⇒169 = 169 + 2a.b

⇒2a.b = 0

⇒a.b = 0

If a.b = 0 then a and b are ⊥ar.

∴Angle between 'a' and 'b' = π/2