51. (a) Is the vector (i+j+k) a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case justify your answer. (c) If A = a(3.0i + 4.0j), where $\boldsymbol{a}$ is a constant, determine the value of $a$ that makes $\vec{A}$ a unit vector.

 51. (a) Is the vector (i+j+k)  a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case justify your answer. (c) If A = a(3.0i + 4.0j), where $\boldsymbol{a}$ is a constant, determine the value of $a$ that makes $\vec{A}$ a unit vector.