For the vectors
and
which are unit vectors, the expression given is
−√2. We are looking for the angle
θ between
and
such that
−√2 is a unit vector.
First, let's calculate the magnitude of the vector
−√2b. If this is a unit vector, its magnitude must be 1 . We use the property that the square of the magnitude of the sum (or difference) of two vectors
and
can be found using:
Here,
||=1 and
||=1 because they are unit vectors. Therefore, the expression modifies to:
The equation simplifies to:
We want this magnitude squared to be 1 , hence:
3−2√2‌cos(θ)=1Solving for
cos(θ) :
‌2√2‌cos(θ)=2‌cos(θ)=‌=‌The value of
cos(θ)=‌ corresponds to an angle
θ=‌.
Thus, the correct answer is Option D: