Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.

Solution 16DQ Step 1: The equation for magnitude of an arbitrary vector, xi + y j + zk is, R = x + y + z 2 Step 2: 2 2 2 From the equation for magnitude, we can see that, R = 0 only if, x + y + z = 0 Since x, y and z are real numbers, their square term will be always positive. Therefore, x > 0, y > 0 and z > 0 Our condition is, whether the magnitude will become zero if the components are non zero. For the condition, x + y + z = 0, x, y and z should be zero. 2 2 2 If any of these components are having a non zero value, then, x + y + z 0.