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
Find the unit vector in direction of where
Here,
Therefore the magnitude of vector
Now the unit vector in direction of is,