Plz explain fast.........
Two vectors having equal magnitude . A makes an angle theta with each other. find the magnitude and direction of the resultant.?
Answers
if the 2 angle having equal magnitude making an angle theta they are apart of right angle triangle.
The two vectors whose resultant has to be found out have equal magnitude.
This is the given information along with the value of the included angle between two vectors A which is theta (©)
We,know by cosine rule to calculate the magnitude of resultant vector
Resultant = √A^2 + B^2 + 2AB cos ©
where, A and B are the component vectors whose resultant is to be calculated and also, that © is the included angle between the two vectors A and B.
Therefore, in this case,
Resultant magnitude = √A^2 + A^2 + 2A^2 cos ©
= √2A^2(1+cos ©)
= 2A cos(©/2). since 1+cos© = 2cos^2(©/2)
therefore, the magntiude of resultant will be 2A cos (©/2)
and, the direction will be ©/2 polar angle from either of the two vectors A i.e the resultant will lie on the line containing the acute angle bisector of the two vectors.