Question

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

Answer 1

Answer:

A + B = 8       sum of vectors

A^2 + C^2 = B^2       resultant C perpendicular to A

(8 - B)^2 + 16 = B^2     substitute for A and C

64 - 16 B + B^2 + 16 = B^2

16 B = 80

B = 5 and A = 3      

Answer 2

Answer:

(3).3 m,5 m

Explanation:

Let A and B are the magnitude of two vectors and C be the magnitude of  resultant of two vectors.

We have to find the magnitude of two given vectors

According to question

$A+B =8 m$

$A=(8-B) m$

$\mid C\mid =4 m$

$A^2+C^2=B^2$ (Using pythagorous theorem)

$(8-B)^2+4^2=B^2$

$64-16B+B^2+16=B^2$

Using identity:$(a-b)^2=a^2+b^2-2ab$

$80+B^2-B^2=16B$

$80=16B$

$B=\frac{80}{16}=5m$

$A=8-B=8-5=3m$

Answer:(3).3 m,5 m