OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

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OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-21(a), Exe-21(b), Exe-21(c), Exe-21(d), and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Class:	12th
Subject:	Mathematics
Chapter  :	Ch-21 Vectors of Section -B

Board	ISC
Writer	OP Malhotra, SK Gupta, Anubhuti Gangal
Publications	S.Chand Publications 2020-21

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-: Included Topics :- 

Exe-21(a), 

Exe-21(b), 

Exe-21(c), 

Exe-21(d),

Chapter Test

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OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Vector: Those quantities which have magnitude, as well as direction, are called vector quantities or vectors.
Note: Those quantities which have only magnitude and no direction, are called scalar quantities.

Representation of Vector: A directed line segment has magnitude as well as direction, so it is called vector denoted as 𝐴𝐵⃗ or simply as 𝑎⃗ . Here, the point A from where the vector 𝐴𝐵⃗ starts is called its initial point and the point B where it ends is called its terminal point.

Magnitude of a Vector: The length of the vector 𝐴𝐵⃗ or 𝑎⃗  is called magnitude of 𝐴𝐵⃗ or 𝑎⃗  and it is represented by |𝐴𝐵⃗| or |𝑎⃗ | or a.
Note: Since, the length is never negative, so the notation |𝑎⃗ |< 0 has no meaning.

Direction Cosines: If α, β and γ are the angles which a directed line segment OP makes with the positive directions of the coordinate axes OX, OY and OZ respectively, then cos α, cos β and cos γ are known as the direction cosines of OP and are generally denoted by the letters l, m and n respectively.

Types of Vectors :-

The various types of vectors included in vector algebra for class 12 concepts are

• Zero Vector
• Unit Vector
• Position Vector
• Co-initial Vectors
• Collinear Vectors
• Equal Vectors
• Negative of a Vector

Zero Vector :- A zero vector is a vector when the magnitude of the vector is zero and the starting point of the vector coincides with the terminal point. In other words, for a vector AB⃗ the co-ordinates of the point A are same as that of the point B then the vector is said to be a zero vector and is denoted by 0.

Unit Vector :-A vector which has a magnitude of unit length is called a unit vector. Suppose if x⃗ is a vector having a magnitude x then the unit vector is denoted by x̂ in the direction of the vector x⃗ and has the magnitude equal to 1.

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Exe-21(a)

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Question 1:

Draw a pair of directed segments vector AB and vector XY which are ………………… length, (ii) its direction ?

Question 2:

Simplify the triangle ABC and PQR

(i)………………

………………….

Question 3:

In Fig. given below the various ………………… of the following sums

……………

Question 4:

…………………

……………….

………………….

Question 6:

In fig. given below EFGH is a parallelogram simplify :

……………….

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Exe-21(b)

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Question 1:

Vector OA and vector OB are vectors a band b respectively ……………….

(i) vector OX and

(ii) vector OY

Question 2:

vector OA and OB are vector s a and b respectively ………………. terms of vector a and b.

(i)……………

(ii)…………..

Question 3:

………………….

………………….

Question 5:

Four point A, B, C, D with position vectors ………………. of line AC and BD.

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Exe-21(c)

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Question 1:

If the position vector of a point (-4, -3) be ………………

Question 2:

If P(-1, 3) and Q (2, -7) express the vector ……………….. the magnitude of r.

Question 3:

……………………

…………………..

…………………..

Question 16:

Show that the three point with position vector ……………….. collinear.

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Position Vector :- If O is taken as reference origin and A is an arbitrary point in space then the vector O⃗A⃗ is called as the position vector of the point.

Position vector simply denotes the position or location of a point in the three-dimensional Cartesian system with respect to a reference origin.

Collinear Vectors :- Vectors which lie along the same line or parallel lines are known to be collinear vectors. They are also known as parallel vectors.

Equal Vectors :- Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

Negative of a Vector :- If two vectors are the same in magnitude but exactly opposite in direction then both the vectors are negative of each other. Assume there are two vectors a and b, such that these vectors are exactly the same in magnitude but opposite in direction then these vectors can be given by

a = – b

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Exe-21(d)

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Question 1:

If ………… vectors AB and BA

Question 2:

If vector a = ……………….

Question 3:

Find the sum of the vector ………………. of these vectors.

Question 4:

……………………

……………………

……………………

Question 18:

Show that the points (2, -1, 3), …………………… are collinear.

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Chapter Test

OP Malhotra Vectors ISC Class-12 Maths Solutions Ch-21

Question 1:

Find the magnitude of vector ……………

Question 2:

Find the direction ratio and the …………………

Question 3:

…………………..

……………………

…………………..

Question 10:

Show that the points A, B, and C with position vectors ……………. a right angled triangle.

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-: End of  Vectors S. Chand ISC Class-12 Maths Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions

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