The magnitude of unit vector will change by amount of scalar multiplied. Not direction. Because direction is being fixed after application of unit vector?s calculation. That is vector divided by its magnitude.

First try to make unit vector of AB. Then you will get Cartesian form of unit vector, after that just multiply 750 scalar quantity with it. Which means you are first taking out desired direction and n multiplying scalar to get desired vector in desired direction.

This statement is wrong. It is not possible unless we apply a negative sign to RHS of equation. That is PxQ = -(QxP). It is because, if you curl your wrist from one vector towards anor vector, thumb projected will give direction of cross product. Thus if you reverse direction, a negative sign is necessary.

The multiplication of x, y and z components with ir respective same component give a scalar, equal to 1, i.e. i.i = 1 and j.j = 1, while jxj =0. This is basic principle of vector algebra which needs to apply wherever needed.

Yes, magnitude of resultant of two vectors always depends on angle between m. It might be greater or smaller than one of vector?s length. For perfectly saying, it does depend upon angle between m.

It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing right coordinates we get option d to be correct. Here just interchange of axis?s representor with ir respective axis is creating confusion. Which must be figured out.

For two vectors defined by an arrow with a head and a tail. The length of each vector and angle between m represents ir magnitude and direction of line of action respectively. The head/tip of arrow indicates sense of direction of vector.

For three vectors A, B and D various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

If one is heading towards positive X-axis and or is in or direction opposite to first one, with both having same length and having an angle between m being obtuse, means that direction is to be in direction of eir 1st quadrant or in 4th quadrant.

As we know ?, ? and ? are angles made by x, y and z-axis respectively. Thus y-axis component is zero, or ? = 90?. And thus if angle is giving component to be zero this means vector in that particular axis is perpendicular to that axis.