Question

Two vectors acting in opposite directions have a resultant of 10 units if they act at at 90 degrees then resultant is 50 calculate magnitude of the vectors

Answer 1

Hey mate!

Here's your answer!!

When acting in opposite direction

a²+b²+2abcos180 = 100

a²+b^-2ab=100


√(a²+b²)=50

a²+b²=2500

Now putting 2500 in equation (1)

2500-2ab=100

-2ab=100-2500

-2ab=-2400

ab=1200

Now,

a²+b²+2 × a × b = (a+b)(a+b)

=2500+2400=(a+b)(a+b)

4900=(a+b)^2

or a+b= 70

Now a+b=70

and a-b=10

Solve for a and b

a=70-b

70-2b=10

-2b=10-70

-2b=-60

➡ b=30

➡ a=40

Hence the two vecors are a=40 and b=30 respectively.

$hope \: it \: helps \: you...$
✌ ✌

Answer 2

When acting in opposite direction

a^2+b^2+2abcos180=100

a^2+b^-2ab=100

sqrt(a^2+b^2)=50

a^2+b^2=2500

now putting 2500 in equation 1

2500-2ab=100

-2ab=100-2500

-2ab=-2400

ab=1200

Now

a^2+b^2+2*a*b=(a+b)(a+b)

=2500+2400=(a+b)(a+b)

4900=(a+b)^2

or a+b= 70

Now a+b=70

and a-b=10

Solve for a and b
a=70-b
70-2b=10
-2b=10-70
-2b=-60
b=30
a=40

✔hence the two vecors a=40 and b=30 respectively
HOPE IT HELPS ✌