Find a unit vector in the same direction as the vector a = 4i−2j+ 4k, and another unit vector in the same direction as b = −4i + 3k. show that the vector sum of these unit vectors bisects the angle between a and b. hint: sketch the rhombus having the two unit vectors as adjacent sides.

Answer with Step-by-step explanation:

We are given that

A=4i-2j+4k

B=-4i+3k

Sum of unit vectors=

Sum of unit vectors=

Sum of unit vectors=

Hence, proved.

A unit vector in the same direction as a vector can be obtained by multiplying by the reciprocal of its norm. So and have corresponding unit vectors and ,

They have vector sum

Find the angle between and using the dot product formula:

Then find the angle between either or and :

(and this is half of )