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​

Answer 1

Answer:

The magnitudes of the two vectors are 3 m and 5 m

Explanation:

Le the two vectors are p and q

So according to the problem,

p+q= 8 ...................(i)

and

√p^2+q^2+2pqcosθ=  4^2

or, p^2+q^2+2pqcosθ = 16 ......................(ii)

qsinθ/p+qcosθ=  tan 900= infinity

p+qcosθ= 0

qcosθ= -p

putting it on (ii)

p^2+q^2+2p(-p) = 16

or, p^2 +q^2 - 2p^2=16

or q^2 -p^2 = 16

or (q+p)(q-p)=16

putting the value of (p+q)

8(q-p)=16

(q-p)= 2............(iii)

now adding (i)and (iii) we get,

p+q+q-p= 8+2

or, 2q= 10

or, q= 5

then p= 8-5= 3