Question

2 vectors p and q as sum of 18 and their resultant is 12 .The resultant is perpendicular to smaller of two vector find the value of p and q and angle between them

Answer 1

Answer:

The value of p is 5 and q is 13

Explanation:

According to the problem the sum of two vectors

p+q= 18..(i)

The resultant of two vectors:

√p^2+q^2+2pqcosθ = 12

p^2+q^2+2pqcosθ = 144,...(ii)

Now the angle by the resultant vector is

qsinθ/p+qcosθ= tan 90 degree

p+qcosθ= 0

qcosθ= -p

now put the value in (ii)

q^2- p^2=144

(p+q)(q-p)= 144

18(q-p)=144

(q-p)= 8...(iii)

now by adding (i) and(iii)

p+q+q-p= 18+8

2q= 26

q= 13

now put it on (i)

p= 5