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

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

Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done

In Figure, identify the following vectors. (i) Coinitial (ii) Equal (iii) Collinear but not equal

Compute the magnitude of the following vectors:

Write two different vectors having same magnitude.

Write two different vectors having same direction.

Find the values of x and y so that the vectors are equal

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

Find the sum ofthevectors.

Find the unit vector in the direction of the vector .

Find the unit vector in the directionofvector, where P and Q are thepoints (1, 2, 3) and (4, 5, 6),respectively.

Forgivenvectors,and, find the unit vector in thedirection of thevector

Find a vector in the direction of vector which has magnitude 8 units.

Show that the vectors are collinear.

Find the direction cosines of the vector

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

Show that the vector is equally inclined to the axes OX, OY, and OZ.

Find the position vector of a point R which divides the line joining two points P and Q whose positionvectorsarerespectively, in the ration2:1 (I) internally (II) externally

Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).

Show that the points A, B and C withpositionvectors,, respectively form the vertices of a right angled triangle.

In triangle ABC which of the following is not true: A. B. C. D.

Ifare two collinear vectors, then which of the following areincorrect: A., for some scalar? B. (I) the respectivecomponentsofare proportional (II) both the vectors have same direction, but different magnitudes

Find the angle between twovectors andwithmagnitudesand 2,respectively having.

Find the angle between the vectors

Find the projection of the vector on the vector .

Show that each of the given three vectors is a unit vector: Also, show that they are mutually perpendicular to each other.

Findand,if.

Evaluate the product .

Find the magnitude oftwovectors, having the same magnitude and suchthat the angle between them is 60° and their scalar product is .

Find , if for a unit vector .

Ifaresuchthatis perpendicular to, then find the value of ?.

Show that is perpendicular to , for any two nonzero vectors

If, then what can be concluded aboutthevector?

Ifeithervector,then. But the converse need not be true.Justify your answer with anexample.

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively,then find ?ABC. [?ABC is the angle between the vectors and ]

Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.

Show thatthevectorsform the vertices of aright angledtriangle.

If is a nonzero vector of magnitude ‘a’ and ? a nonzero scalar, then ? is unit vector if (A) ? = 1 (B) ? = –1 (C) (D)

Find , if and .

Find a unit vector perpendicular to each ofthevectorand,where

If aunitvectormakesanangleswithwithand an acute angle ? with , then find ? and hence, the compounds of.

Show that

Find ? andµif.

Given that and . What can you conclude about the vectors ?

Letthevectorsgivenas. Then show that

Ifeitheror,then. Is the converse true? Justify your answer withan example.

Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).

Find the area of the parallelogram whose adjacent sides are determined by the vector .

Letthevectorsandbesuchthatand,thenis a unit vector, if theanglebetweenandis (A) (B) (C) (D)

Area of a rectangle having vertices A, B, C, and D with position vectors andrespectivelyis (A)(B)1(C) 2 (D)

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

Find the scalar components and magnitude of the vector joining the points .

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

If , then is it true that ? Justify your answer.

Findthevalueofxforwhichisa unitvector.

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors .

If, find a unit vector parallel tothe vector.

Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Find the position vector of a point R which divides the line joining two points P and Q whose positionvectorsareexternally in the ratio 1: 2. Also,show that P is the mid point of the line segmentRQ.