Question

the resultant of two vectors is perpendicular to the one of them and has magnitude 4m. if the sum of the magnitude of two vectors is 8 then thieir respective magnitude are 1)4m ,4m 2) 2m, 6m 3)3m ,5m 4)1m , 7m​

Answer 1

answer : option (3) 3m, 5m

explanation : let A and B are two vectors.

given, |A| + |B| = 8 .....(1)

and |A + B| = √{|A|² + |B|² + 2|A|.|B|cosθ} = 4 ....(2)

also, A.(A + B) = 0 or, B.(A + B) = 0

A.(A + B) = 0

or, |A|² + A.B = 0

or, -|A|² = A.B = |A|.|B|cosθ, where θ is angle between A and B.

so, cosθ = -|A|/|B|

now, from equation (2),

√{|B|² - |A|²} = 4

squaring both sides,

|B|² - |A|² = 16

or, (|B| - |A|})(|B| + |A|) = 16

from equation (1),

(|B| - |A|) × 8 = 16

(|B| - |A|) = 2 ......(3)

from equations (1) and (3),

|B| = 5 and |A| = 3

hence, option (3) is correct choice.