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NCERT Class 12 Maths Chapter 10: Vector Algebra 19 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Miscellaneous Exercise

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Write a unit vector in the XY-plane making 30° with positive x.

Find scalar components and magnitude of the displacement from P(x₁,y₁,z₁) to Q(x₂,y₂,z₂).

A girl walks 4 km west, then 3 km at 30° east of north. Find her net displacement.

If a=b+c, must |a|=|b|+|c|? Justify.

Find x so x(i+j+k) is a unit vector.

Find a magnitude-5 vector parallel to the resultant of a=2i+3j−k and b=i−2j+k.

For a=i+j+k, b=2i−j+3k, c=i−2j+k, find a unit vector parallel to 2a−b+3c.

Show A(1,−2,−8), B(5,0,−2), C(11,3,7) are collinear and find AB:BC.

P,Q have position vectors 2a+b and a−3b. Find R dividing PQ externally in ratio 1:2, and show P is the midpoint of RQ.

Adjacent sides of a parallelogram are (2,−4,5) and (1,−2,−3). Find unit vector(s) parallel to its diagonal(s) and its area.

Show the direction cosines of a nonzero vector equally inclined to OX,OY,OZ are ±(1/√3,1/√3,1/√3).

For a=(1,4,2), b=(3,−2,7), c=(2,−1,4), find d perpendicular to a,b with c·d=15.

The dot product of i+j+k with a unit vector along the sum (2,4,−5)+(λ,2,3) is 1. Find λ.

If a,b,c are mutually perpendicular nonzero vectors of equal magnitudes, show that a+b+c is equally inclined to a,b,c.

For nonzero a,b prove (a+b)·(a+b)=|a|²+|b|² iff a,b are perpendicular.

For the angle θ between nonzero vectors a,b, when is a·b≥0?

Unit vectors a,b make angle θ. When is a+b also a unit vector?

Evaluate i·(j×k)+j·(i×k)+k·(i×j).

For nonzero vectors a,b, at which listed angle is |a·b|=|a×b|?