If and angle between is twice the angle between then show that where is the angle between
It is given that angle between is
Therefore the angle between will be
Here,
∴
.
Hence proved.
Find a vector having magnitude equal to the magnitude of vector and parallel to vector
Magnitude of vector A is,
Unit vector in direction of vector
The vector that has magnitude same as that of vector and parallel to vector
Prove that:
, where is the angle between
By using distributive and commutative law, the dot product can be evaluated as,
That is,
If then do you think that A is necessarily equal to C?
Given that,
Let angle between be and that between
∴
Now, if then A = C, and
then
Thus A is not necessarily equal to C.