Find the unit vector in direction of where
Here,
Therefore the magnitude of vector
Now the unit vector in direction of is,
Show that
and are perpendicular to each other.
Given,
and
have to be perpendicular to each other.
To prove that we will find the dot product.
Hence .
Since, the dot product is zero the two vectors are perpendicular to each other.
What is the angle between the vectors and ?
Given that,
and
Let be the angle between the given two vectors.
We know,
∴
Now
Magnitude is given by,
Thus, angle between the vectors,
A particle moves from point (2, 3, 5) to (8, -4, 2) when a force of unit is applied on it. Find the work done by the force.
Given, a particle moves from point P(2,3,5) to Q(8,-4,2).
Force applied on th particle, F =
Therefore, the displacement undergone by the particle is,
Therefore work done by force is,
J