Vector A has magnitude of 10, B has mag of 20. They're perpendicular. What is A + B?

Vector A with magnitude 10 starts at the origin and is going to the right along the x-axis. Vector B with magnitude 20 starts at the origin and is going down along the x axis. Between them is a RESULTANT VECTOR "C" that forms a 30 degree angle and 60 degree angle between A %26amp; B, respectively. I found that the coordinates of C would be (10, -20) and that the magnitude of C is (sqrt of (10^2 + -20^2) = sqrt 500. Is this correct?

Vector A has magnitude of 10, B has mag of 20. They're perpendicular. What is A + B?
i have taken vector 20 along the 'x' axis from the origin and vector10 along the 'y' axis from the origin,both in the positive directions i.e.20 unit vector due east and 10 unit vector due north.


by the rectangle law of vectors the magnitude of the resultant vector will be given by the diagonal of the rectangle and using the pythagoras theorem the diagonal will be sq.rt.of 20^2+10^2


=sq.rt.of 500=10root5


for finding the direction 'tangent' of the angle the resultant makes with the 20 unit vector will be 10/20=1/2


so the direction will be tan inverse 1/2


what you have done is correct except for a small clerical error


Vector B with magnitude 20 starts at the origin and is going down along the 'y' axis and not 'x'axis as you have written


also it will form a -63.5 degree angle with A and not as you have depicted.hope you don't mind being corrected
Reply:Yes your answes is correct based on the process of getting the vector sum or resultant given two vectors. But to simplify your answer either get the square root=22.3607 or A+B = 10sqrt of 5





Further explanation:


The figure formed based on the problem is a right triangle with hypotenuse representing the unknown A+B. So, to solve the unknown quantity we use the formula of Pythagorean Theorem which states that the hypotenuse of a given right traingle is equal to the square root of of the sum of the squares of the other two sides or legs of the said triangle.
Reply:Yes, but I think you mean vector B goes down along the y-axis, not the x-axis
Reply:The magnitude of sqrt(500) is correct, but all vectors have both a magnitude and direction. The direction of the resultant vector is down and to the right or 300 degrees.
Reply:The magnitude is 50 indeed. However a vector also has a direction, which you have to mention. If the angle betrween A and A+B is a,


then tan(a) = 20/10 = 2, so a=63 degrees.


So your mentioned angles are wrong.
Reply:it is correct except for the angles you stated. The correct angle between the x axis and the resultant vector is the arctan of 20/10 or 63.43 degrees and the angle between the y axis and the resultant vector is the arctan of 10/20 or 26.57 degrees.
Reply:PERFECTLY!!!