Question

Find a unit vector parallel to the resultant of the vectors a=i+4j-2k and b = 3i-5j+k

Answer 1

ans___ 4i-j-k/3 root 2

Answer 2

Given: vector a = i + 4j -2k and vector b = 3i-5j+k

To Find: Unit vector parallel to the resultant of a and b vector

Solution:

Let c be the resultant of a and b

c = a + b

c = i + 4j - 2k + 3i -5j +k

c = i + 3i + 4j - 5j -2k + k

c = 4i - j -k

A unit vector is a vector having only a direction and its magnitude is one.

So to obtain the unit vector, we divide the vector by its magnitude

|c| = √(4)² + (-1)² + (-1)²

|c| = √16 + 1 + 1

|c| = √18

|c| = √(3)²(2)

|c| = 3√2

Unit vector of c = c vector/magnitude of c vector

Unit vector of c = $\frac{4i - j -k}{3\sqrt{2} }$

Therefore, the unit vector of c is  $\frac{4i - j -k}{3\sqrt{2} }$.