If A, B, C, D are the points with position vectors respectively, find the projection of along .

Given are points, A, B, C and D.

Let O be the origin.

We have,

Position vector of A

Position vector of B

Position vector of C

Position vector of D

Now, let us find out and .

Position vector of B-Position vector of A

And,

Position vector of D-Position vector of C

The projection of along is given by,

[∵ we know that, and .

So,

Also, we know that, ]

Multiply numerator and denominator by √21.

⇒ Projection = √21

Thus, projection of along is √21 units.