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,
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.
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
For what value of c the vector will be perpendicular to:
(i) Z-axis (ii) Y-axis?
(i) Vector is zero.
i.e.
The equation is satisfied for all values of c.
Therefore is always perpendicular to Z-axis whatever the value of c.
(ii) Similarly
∴ is perpendicular to Y-axis if c = 0.