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# Chapter 10 Vector Algebra

Quantities which have only magnitude are called scalars. But quantities that involve magnitude and direction are called vectors. Discussion will be on algebra of vectors. Topics which covered in this chapter - vectors, scalars, direction cosines and direction ratios of a vector, Types of vectors, position vector of a point , negative of a vector, addition of vectors, multiplication of a vector by a scalar, dot and cross products, scalar triple product of vectors.

Download pdf of NCERT Solutions for Class Mathematics Chapter 10 Vector Algebra

Download pdf of NCERT Examplar with Solutions for Class Mathematics Chapter 10 Vector Algebra

### Exercise 1

•  Q1 Represent graphically a displacement of 40 km, 30° east of north. Ans: \begin{align}Here, vector\;\overrightarrow{OP}\; represents \;the\; displacement\; of \;40\; km, 30° East \;of \;North.\end{align} Q2 Classify the following measures as scalars and vectors. (i) 10 kg (ii) 2 metres north-west (iii) 40° (iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2 Ans: (i) 10 kg is a scalar quantity because it involves only magnitude. (ii) 2 meters north-west is a vector quantity as it involves both magnitude and direction. (iii) 40° is a scalar quantity as it involves only magnitude. (iv) 40 watts is a scalar quantity as it involves only magnitude. (v) 10–19 coulomb is a scalar quantity as it involves only magnitude. (vi) 20 m/s2 is a vector quantity as it involves magnitude as well as direction. Q3 Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done Ans: (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. Q4 In Figure, identify the following vectors. (i) Coinitial (ii) Equal (iii) Collinear but not equal Ans: \begin{align} (i) \;Vectors\; \overrightarrow{a}\; and\; \overrightarrow{d}\; are \;coinitial\; because\; they\; have\; the\; same \;initial \;point. \end{align}  \begin{align}(ii)\; Vectors\;\overrightarrow{b} \;and\;\overrightarrow{d}\; are\; equal\; because\; they\; have\; the\; same \;magnitude \;and\; direction. \end{align}  \begin{align}(iii)\; Vectors\;\overrightarrow{a} \;and\; \overrightarrow{c} \;are\; collinear\; but\; not\; equal\;. This\; is\; because\; although\; they\; are \;parallel,\; their\; directions\; are\; not \;the\; same.\end{align} Q5 Answer the following as true or false.  \begin{align}(i) \overrightarrow{a}\;  and\; \overrightarrow{-a}\; are\; collinear.\end{align} (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. Ans: (i) True.  \begin{align}(i) \overrightarrow{a}\;  and\; \overrightarrow{-a}\; are\; collinear.\end{align} (ii) False. Collinear vectors are those vectors that are parallel to the same line. (iii) False. It is not necessary for two vectors having the same magnitude to be parallel to the same line. (iv) False. Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.

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