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# Xam Idea Class 12 Maths Chapter 11 Solutions: Vector Algebra

Xam Idea Class 12 Maths Solutions for Chapter 11 ‘Vector algebra’ is one of the best guides available for preparing this chapter for CBSE Class 12 board exams. Our Xam Idea Solutions are famous for their well-composed syllabus along with enriched content with topics in much simpler language for your better understanding. You might have already come across vectors while studying physics. Our solutions will help you learn more about vectors, types of vectors, components of a vector along with addition, subtraction and multiplication of vectors.

Xam Idea Class 12 Maths Solutions for Vectors comprises 87 questions. These questions are divided into three categories, namely Very short answer questions (one mark), Short answer questions (two marks) and Long answer questions (4 marks). You will be able to solve questions related to properties and applications of vector products (i.e. Scalar product and Dot product). You will also learn about Triple vector products which are required to calculate the volume of a parallelepiped.

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## Important topics for Xam Idea Class 12 Maths Solutions Chapter 11: Vector Algebra

Vector algebra is important and also an easy topic in mathematics which can be easily covered if you learn it from Xam Idea Class 12 Maths Chapter 11: Vector algebra, and refer Instasolv for solutions at the same time. You must prepare the following topics.

Scalars and Vectors:

Scalars and Vectors both are different as Scalar only have a magnitude, whereas vectors have both magnitudes as well as directions.

Magnitude and Direction of Vector

A vector can be represented by the length of its magnitude on a plane with an arrow which points towards the direction of the vector.

Types of Vectors

Vectors can also be further classified among the following:

1. Equal vectors – Consider there are two vectors if they have the same magnitude as well as the direction anywhere on the plane, then such vectors can be considered as equal vectors.
2. Unit vectors – let there be a vector a, then a unit vector in the same direction of a has the magnitude of unit value.
3. Zero vectors – A zero vector or also known as a null vector is denoted as 0. The magnitude of a zero vector is zero obviously, with no direction.
4. Parallel vectors – Two vectors A and B are considered as parallel vectors if they are moving in the same direction and there exists a constant k other than 0, which satisfies the following equation of scalar product. A = k B
5. Collinear vectors – When two or more vectors lie alongside to the same line, such vectors are called collinear vectors.

In this topic, The laws you will learn about the basic laws of vectors addition, which are as follows:

Triangular law of vector addition states that if we try to represent two vectors as two sides of a triangle (make sure the order is similar), then the resultant vector should be the same as the third side of the triangle in terms of magnitude and the direction.

The Parallelogram law of vector addition, states that if we represent two vectors as two adjacent sides of a parallelogram, then the diagonal vector from the point of contact of two vectors is the resultant of the two vectors.

Multiplication of a Vector by a Scalar

In the case of multiplication of a vector by a scalar, the magnitude of the resultant vector gets multiplied by that of the scalar whereas the direction of the vector is the same that of the initial vector.

Scalar (dot) Product of Vectors

The scalar or dot product of two vectors p and q is:

Where, θ is the angle between the given vectors

Special cases:

When q = 0°, then both vectors are parallel to each other hence the scalar product becomes p.q (cos 0° = 1).

When q = 90°, then both vectors are perpendicular to each other hence the scalar product becomes 0 (cos 90° = 0).

Vector (cross) Product of Vectors

The vector or cross product of two vectors and with an angle θ between them of  is:

where n is the unit vector perpendicular to both vectors p and q

Special cases:

When q = 0°, then both vectors are parallel to each other hence the vector product becomes  0. (sin 0° = 0).

When q = 90°, then both vectors are perpendicular to each other hence the vector product becomes p.q (cos 90° = 0).

Scalar Triple Product of Vectors

Let there be a parallelepiped with sides represented by P, Q and R. Then the volume of the parallelepiped is represented by the scalar triple vector product of the given vectors.

### Exercise Discussion for SL Loney Plane Trigonometry Solutions Chapter 11: Vector Algebra

Xam Idea Class 12 Maths Chapter 11 ‘Vector Algebra’ consists of a total of 87 questions for your practice. These questions are further divided into 3 sections. Every section carries different marks. Let’s see each section in detail.

• This section consists of one section of previous year questions which has 23 questions in it. Questions in this section generally come for 1 mark and are very easy to attempt if you have good knowledge about the chapter.
• You will see easy questions like to find the magnitude of the given vector, find the missing value in the vector for a given condition.

• In Short answer questions, every question consists of 2 marks each.
• There are 13 questions in this section that are similar to questions you face in the very short answer questions sections but, a bit trickier.