Important Questions for Class 12 Maths Chapter 10 – Vector Algebra

1)

Ans – Given that

Ans – Given that

Ans – Given that

Ans –

Ans – Initially, we compute the cross product of the given two vectors:

The required unit vector that is perpendicular to both given vectors can be determined as

Ans – Given that

For a vector, the dot product with itself is equal to the square of its magnitude.

Ans – Given that ABCDEF is a regular hexagon we know,

Applying the triangle law of addition, we obtain

Ans – Sum of vectors is obtained as,

By squaring LHS and RHS we get:
⇒ (λ + 6)² = λ² + 4λ + 44
⇒ λ² + 12λ + 36 = λ² + 4λ + 44
⇒ λ² + 12λ + 36 = λ² + 4λ + 44
⇒ 8λ = 8
⇒ λ = 1

Ans – Given that

NCERT Questions for Class 12 Maths Chapter 10 – Vector Algebra

Many students fear Vector Algebra, but don’t worry, for there are ways to improve your understanding and shine in this subject. One such method is the practice of important questions that cover key concepts and help you build confidence in solving problems.

Importance of Vector Algebra in Class 12 Mathematics

Vector Algebra plays a very important role in mathematics, especially in Class 12. It is used to represent quantities that have both magnitude and direction, thus making it a powerful tool for solving various problems in physics, geometry, and engineering. It helps you do well in your math exams but also lays a strong foundation for higher studies in calculus, mechanics, and computer graphics.

Vector Algebra introduces the concepts of vector addition, scalar multiplication, dot and cross products, and vector equations-all of which are crucial for solving complex problems in mathematics and physics. By mastering Vector Algebra, you can improve your problem-solving skills, analytical thinking, and overall mathematical fluency.

Importance of Practicing Important Questions

To achieve skill in Vector Algebra, practicing through important questions would be highly helpful. Since questions are thoroughly picked to present wide-ranging ideas as well as broad ranges of difficulties, solving the important questions reinforces your concept understanding and assesses your knowledge based on numerous examples. It further helps to ascertain your area of strength and weaknesses, work out on critical points that are weaker, and you will eventually have confidence when such problems crop up in your examinations.