NCERT Solutions for Class 12 Maths Chapter 10: Vector Algebra - Exercise 10.1

1. Represent graphically a displacement of $40{\text{km}},{30^\circ }$ east of north.

Ans:

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Here, vector OP represents the displacement of $40\;{\text{km}},{30^ \circ }$ East of North.

2. Classify the following measures as scalars and vectors.

(i) $10\;{\text{kg}}$

Ans: $10\;{\text{kg}}$ is a scalar quantity because it involves only magnitude.

(ii) 2 meters north-west

Ans:  2 meters north-west is a vector quantity as it involves both magnitude and direction.

(iii) ${40^\circ }$ 

Ans: ${40^\circ }$ is a scalar quantity as it involves only magnitude.

(iv) 40 watt 

Ans: 40 watts is a scalar quantity as it involves only magnitude.

(v) ${10^{ - 19}}$ coulomb

Ans: ${10^{ - 19}}$ Coulomb is a scalar quantity as it involves only magnitude.

(vi) $20\;{\text{m}}/{{\text{s}}^2}$

Ans: $20\;{\text{m}}/{{\text{s}}^2}$ is a vector quantity as it involves magnitude as well as direction.

3. Classify the following as scalar and vector quantities.

(i) Time Period

Ans: Time period is a scalar quantity as it involves only magnitude.

(ii) Distance

Ans: Distance is a scalar quantity as it involves only magnitude.

(iii) Force 

Ans: Force is a vector quantity as it involves both magnitude and direction.

(iv) Velocity

Ans: Velocity is a vector quantity as it involves both magnitude as well as direction.

(v) Work Done

Ans: Work done is a scalar quantity as it involves only magnitude.

4. In Figure, identify the following vectors.

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(i) Co-initial

Ans: Vectors $\overline {\text{a}} $ and $\overline {\text{d}} $ are co-initial because they have the same initial point.

(ii) Equal

Ans: Vectors ${\text{b}}$ and ${\text{d}}$ are equal because they have the same magnitude and direction.

(iii) Collinear but not equal

Ans: Vectors $\overline {\text{a}} $ and $\overline {\text{c}} $ are collinear but not equal. This is because although they are parallel, their directions are not the same

5. Answer the following as true or false:

(i) a and - a are collinear.

Ans: True.

Vectors a and - a can be parallel or coinciding vectors. Either way the vectors will have same magnitude but opposite in direction and will be parallel to the same line.

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

Ans: False. 

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

(iii) Two vectors having same magnitude are collinear.

Ans: False.

It is not necessary for two vectors having the same magnitude to be parallel to the same line.

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

Ans: False.

Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1

Opting for the NCERT solutions for Ex 10.1 Class 12 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 10.1 Class 12 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 12 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 12 Maths Chapter 10 Exercise 10.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 12 Maths Chapter 10 Exercise 10.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.

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