Let's break down the problem step by step.
1. Finding the Sum of the Vectors
The sum of the two vectors is:
2. Finding the Unit Vector
To find the unit vector parallel to the sum, we need to divide the sum by its magnitude:
Magnitude of the sum:
Unit vector:
3. Scalar Product
The scalar product (dot product) of the vector
++ with the unit vector is given by:
4. Setting the Scalar Product to Unity
We are given that this scalar product is equal to unity (1):
=1 5. Solving for 'b'
Simplifying the equation and solving for '
b ':
b+6=√b2+4b+44Squaring both sides:
b2+12b+36=b2+4b+448b=8b=1Therefore, the value of '
b ' is 1 , which corresponds to Option D.