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NCERT Class 12- Mathematics: Chapter β 10 Vector Algebra Part 2
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 Rβ² 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 Ξ» 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