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Mathematics Class 12 NCERT Solutions: Chapter 10 Vector Algebra Part 1

Illustration: Mathematics Class 12 NCERT Solutions: Chapter 10 Vector Algebra Part 1

Exercise: 10.1

Q: 1. Represent graphically a displacement of 40 km, 30° east of north.

Answer:

Illustration: Mathematics Class 12 NCERT Solutions: Chapter 10 Vector Algebra Part 1

Here, Vector represents the displacement of , East of North.

Q: 2. Classify the following measures as scalars and vectors.

(i)

(ii) 2 metres north-west

(iii)

(iv)

(v)

(vi)

Answer:

(i) is a scalar quantity because it involves only magnitude.

(ii) meters north-west is a vector quantity as it involves both magnitude and direction.

(iii) is a scalar quantity as it involves only magnitude.

(iv) is a scalar quantity as it involves only magnitude.

(v) is a scalar quantity as it involves only magnitude.

(vi) is a vector quantity as it involves magnitude as well as direction.

Q: 3. Classify the following as scalar and vector quantities.

(i) Time Period

(ii) Distance

(iii) Force

(iv) Velocity

(v) Work done

Answer:

(i) Time period is a scalar quantity as it involves only magnitude.

(ii) Distance is a scalar quantity as it involves only magnitude.

(iii) Force is a vector quantity as it involves both magnitude and direction.

(iv) Velocity is a vector quantity as it involves both magnitude as well as direction.

(v) Work done is a scalar quantity as it involves only magnitude.

Q: 4. In Figure, identify the following vectors.

Illustration: Mathematics Class 12 NCERT Solutions: Chapter 10 Vector Algebra Part 1

(i) Coinitial

(ii) Equal

(iii) Collinear but not equal

Answer:

(i) Vectors and are coinitial because they have the same initial point.

(ii) Vectors and are equal because they have the same magnitude and direction.

(iii) Vectors and are collinear but not equal. This is because although they are parallel, their directions are not the same.

Q: 5. Answer the following as true or false.

(i) and are collinear.

(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.

Answer

(i) True.

Vector are parallel to the same line.

(ii) False.

Collinear vectors are those vectors that are parallel to the same line.

(iii) False.

It is not necessary, to having same magnitudes for collinear vectors. Collinear vectors are parallel to each other, or we can say collinear vectors are parallel to the same line.

(iv) False.

Two vectors are said to be equal, if they have the same magnitude and the same direction, regardless of the position of their initial points. i.e.. Vectors and are collinear and having same magnitudes, but they are not equal vectors.

Exercise 10.2

Q: 1. Compute the magnitude of the following vectors:

Answer:

The given vectors are: