NCERT Solutions Class 12 Mathematics Chapter 10 Download In Pdf

Chapter 10 Vector Algebra Download in pdf

**Question 1.** Represent graphically a displacement of 40 km, 30° east of north.

**Question** 2. Classify the following measures as scalars and vectors.

(i) 10 kg

(ii) 2 meters north-west

(iii) 40°
(iv) 40 watt

(v) 10–19 coulomb

(vi) 20 m/s2

**Question 3.** Classify the following as scalar and vector quantities.

(i) time period

(ii) distance

(iii) force

(iv) velocity

(v) work done

**Question 4.** In Fig 10.6 (a square), identify the following vectors.

(i) Coinitial

(ii) Equal

(iii) Collinear but not equal

**Question 5.** Answer the following as true or false.

(i) a
and −a are collin
ear.

(ii) Two collinear vectors are always equal in
magnitude.

(iii) Two vectors having same magnitude are collinear.

(iv) Two collinear vectors having the same magnitude are equal.

**Question 2.** Write two different vectors having same magnitude.

**Question 3. **Write two different vectors having same direction.

**Question 4. **Find the values of x and y so that the vectors 2iˆ + 3 ˆj and xiˆ + yˆj are equal.

**Question 5. **Find the scalar and vector components of the vector with initial point (2, 1) and
terminal point (– 5, 7).

**Question 6.** Find the sum of the vectors a = iˆ − 2 ˆj + kˆ, b = −2iˆ + 4 ˆj + 5kˆ and c� = iˆ − 6 ˆj – 7kˆ .

**Question 7.** Find the unit vector in the direction of the vector a = iˆ + ˆj + 2kˆ .

**Question 8. **Find the unit vector in the direction of vector PQ,
where P and Q are the points
(1, 2, 3) and (4, 5, 6), respectively.

**Question 9.** For given vectors, a = 2iˆ − ˆj + 2kˆ and b = −iˆ + ˆj − kˆ , find the unit vector in the
direction of the vector a + b .

**Question 10. **Find a vector in the direction of vector 5iˆ − ˆj + 2kˆ which has magnitude 8 units.

**Question 11.** Show that the vectors 2iˆ − 3 ˆj + 4kˆ and − 4iˆ + 6 ˆj − 8kˆ are collinear.
12. Find the direction cosines of the vector iˆ + 2 ˆj + 3kˆ .

**Question 13.** Find the direction cosines of the vector joining the points A(1, 2, –3) and
B(–1, –2, 1), directed from A to B .

**Question 14.** Show that the vector iˆ + ˆj + kˆ is equally inclined to the axes OX, OY and OZ.

**Question 15.** Find the position vector of a point R which divides the line joining two points P
and Q whose position vectors are iˆ + 2 ˆj − kˆ and – iˆ + ˆj + kˆ respectively, in the
ratio 2 : 1

(i) internally

(ii) externally

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- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 6 Application of Derivatives
- Chapter 7 Integral
- Chapter 8 Application of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three Dimensional Geometry
- Chapter 12 Linear Programming
- Chapter 13 Probability

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