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NCERT Solutions for Class 12 Maths (With Examples, Misc) - Teachoo

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Class X Mathematics Notes. Contains solved exercises, review questions, MCQs, important board questions and chapter overview. Class 10 Maths Notes. Chapter 1 - Quadratic Equation Overview Exercise 1.

Chapter 3 - Variations Overview Exercise 3. Chapter 4 - Partial Fractions Overview Exercise 4. Chapter 6 - Class 12 maths ch 10 miscellaneous act Statistics Overview Exercise Class 11 Maths Ch 10 Miscellaneous Meaning 6. Chapter 7 - Introduction to Trignometry Overview Exercise 7.

Chapter 9 - Chords of a Circle Overview Exercise 9. Chapter 10 class 12 maths ch 10 miscellaneous act Tangent to a Circle Overview Exercise If you find any mistake or any problem with the notes, please send us an email at [email protected] Advertisement.

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Simply said:

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Hence, vector which is also perpendicular to both and is where or some other scalar. Now given and. Putting in eq. Let , and. Also given Dot product of and is 1. Given: are mutually perpendicular vectors of equal magnitude.

And say ���. Let vector make angles with vectors respectively. We know that. Similarly, and. Therefore, is equally inclined to the vectors and. Now if and are perpendicular. Putting in. But given. Therefore, vectors and are perpendicular to each other. If is the angle between two vectors and then only when:.

Let and be two unit vectors and is the angle between them. Then is a unit vector if:. Given: and are unit vectors. Vector equation of the required line is. Direction ratios of line AB are. A vector along the line AB is.

Similarly, direction ratios of line CD are. Given: Equation of one line is. Direction ratios of this line are its denominators, i. Again, equation of second line is. Position vector say of point P is 1, 2, 3. Equation of the given plane is. Comparing with. Since, the required line is perpendicular to the given plane, therefore, vector along the required line is. Equation of the required line is. Equation of any plane parallel to the plane is �..

Plane i passes Ch 3 Maths Class 10 Teachoo Act through. Putting in eq. Putting the value of in eq. Given: Vector equation of one line is. Comparing with we get. Again given: Vector equation of another line is. We know that length of shortest distance between two skew lines is..

Putting these values in eq. Direction ratios of this line AB are. Equation of the line AB is. Thus, required point is P. Direction ratios of the line joining the points A and B are. Equation of the line AB are ��� i.

Equation of the plane is ��� ii. From eq. Putting the values of in eq. Thus, required point of intersection is. So, this is a vector quantity. In Class 11 Maths Ch 10 Miscellaneous Ideas this chapter, we will talk about vectors. Serial order wise Ex Ex Supplementary examples and questions from CBSE. Scalar or vector. Graphical displacement. Type of vector. Multiplication of a vector by a scalar.

Equal vectors. Unit vector. Direction cosines and ratios.

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