# NCERT Class 12-Mathematics: Chapter – 10 Vector Algebra Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 3**:

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors respectively, in the ratio , (i) internally and (ii) externally.

**Answer**:

(i) The position vector of the point R dividing the join of P and Q internally in the ratio is given by

(ii) The position vector of the point R′ dividing the join of P and Q in the ratio externally is given by

**Question 4**:

If the points , and are collinear, find the value of .

**Answer**:

Let the given points be and . Then

And

Since A, B, C, are collinear, we have

Therefore

**Question 5**:

Find a vector of magnitude units which makes an angle of and with and axes, respectively.

**Answer**:

Here

Therefore,

Hence, the required vector is given by

.

**Question 6**:

If , find λ such that is perpendicular to

**Answer**:

We have

Since

**Question 7**:

Find all vectors of magnitude that are perpendicular to the plane of and .

**Answer**:

and . Then

Therefore, unit vector perpendicular to the plane of and is given by

Hence, vectors of magnitude of that are perpendicular to plane of and are