Let represent any nonzero vector. Why is a unit vector, and what is its direction? If ? is the angle thamakes with the + x -axis, explain why is called the direction cosine for that axis.
Solution to 21DQ Here in the first part of the solution we would enquire about Unit Vector and its direction.In the second part we would see why(A) .i is a direction cosine in that axis. PART 1 Step 1. Mathematically a vector is defined as a dot product of its magnitude and its direction. =|A|.A Here A t he component that gives the direction of the vecto. he magnitude is given by | | Step 2. Unit vector is a vector with a magnitude 1 and gives the information of the direction of the vector it is associated with. Thus to find the direction of a vector, it is necessary to find its unit vector. A A= .A The unit vector itself gives the direction. 1 1 For example A= (2, 2) is a unit vector. It has a magnitude of 1. Its direction is1 i - 1 j . 2 2 PART 2 Step 1. Consider the vector A is making an angle with respect to x axis. Direction cosine is the cosine of the angle between the two vectors.