Vector Algebra: Vector Addition(20 Nov) - JEE MCQ

The internal bisector 

Since, are non-coplanar
are also non-coplanar.
So, any vector can be expressed as a linear combination of these vectors.

Since, and are mutually perpendicular vectors, therefore any vector can be expressed in terms of and

Taking dot product with   in eq. (1), we get

Taking dot product with   in eq. (1), we get

Let be the origin and the bisector of meets at . Then and position vector of is given by

Letthe required vector is .

As the threevectors  are coplanar so one must be linear combination of other twoi.e,

Oncomparison, we get

Only option  has a = 1, b = −1, c = −2 such that a + c = 1 − 2  = −1 = b ⇒ b = a + c
So, the required vector is 

If two vectors are perpedicular to each other then their dot product is equal to 0.

Here, vector is perpendicular to

Given that

Let P.V. of

Let and be unit
respectively, then  and

The required vector