Question

two vectors acting in the opposite direction have a resultant of 10 if they act at 90 degree to each other then the resultant is 50 calculate magnitude of vectors

Answer 1

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.