When a pair of vectors are at right angles, is the resultant always greater in magnitude than either of the vectors separately?

Solution 22RQ Introduction Vector is a quantity which is having both magnitude and direction. If two vectors X and Y are come into the picture, the resultant of those vectors should be, 2 2 R = (x + y + 2xy cos ) Where is the angle between the two vectors. Step 1 Here, they have provided, the two vectors are at right angles. So, = 90° Hence, cos = cos 90 = 0 Therefore, according to our equation, the resultant of the vectors X and Y at right angles should be, 2 2 R = (x + y ) The magnitude of the vector X is, “x” and the magnitude of vector Y is “y”. Suppose, x = 1 and y = 1 2 2 The resultant, R = 1 + 1 = 2 Conclusion So, the resultant of two vectors at right angle is greater than that of either of the two vectors.