Question

Find the magnitude and the direction of the resultant of two vectors A and B in terms of their magnitudes and angle e between them.​

Answer 1

Answer:

this is answer of your questions 1or 2

Answer 2

Answer:

To know the resultant vector magnitude and its angle between, simply apply the triangle law of vector addition. Assume the two vector A and B with an angle alpha whose resultant be vector C given by vector C = vector A + vector B. In addition drop a line from the point B and C meeting to form the right angled triangle, so AC ^2 = AD ^2 + CD ^2

=> AC = \sqrt{ AD ^2 + CD ^2 }

=> AC = \sqrt{ ( AB + BD) ^2 + CD ^2}

=> AC = \sqrt{ Ab ^2 + 2 AB x BD + BD ^2 + CD ^2 }

=> From triangle BCD, cos alpha = BD / BC

=> BD = BC \times cos \alpha

=> AC = \sqrt{a^2 + 2 ab cos \alpha + BC ^2}

=> AC = \sqrt{a ^2 + b ^2 + 2 a b cos \alpha}

=> c = \sqrt{a ^2 + b ^2 + 2 a b cos \alpha}

The resultant vector makes angle theta therefore, in triangle BCD,

sin \alpha = CD / BC

=> CD = BC sin \alpha,

and in triangle ADC,

tan \theta = CD / AD = BC sin \alpha / a + b cos \alpha

=> \theta = tan ^{-1} b sin \alpha / a + b cos \alpha.