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NCERT Solutions for Class 12 Maths (With Examples, Misc) - Teachoo
The Class 12 Maths Formulas provided here will assist you in conquering your Board exams Class 12 Maths Ch 10 Miscellaneous Vol as well as the entrance examinations. Let�s take a look at the important chapters of Class 12 Maths for which we need formulas: Relations and Functions. Inverse Trigonometric Functions.� Definition/Theorems. Empty relation holds a specific relation R in X as: R = ? ? X ? X. A Symmetric relation R in X satisfies a certain relation as: (a, b) ? R implies (b, a) ? R. A Reflexive relation R in X can be given as: (a, a) ? R; for all ? a ? X. A Transitive relation R in X can be given as: (a, b) ? R and (b, c) ? R, thereby, implying (a, c) ? R. A Universal relation is the relation R in X can be given by R = X ? X. Equivalence relation R in X is a relation that shows all the reflexive, symmetric and transitive relations. Select chapter number to view Class 12 Maths NCERT chapter wise solutions.� This chapter introduces the concept of Differential equations, the general and particular solutions, and the order and degree of an equation. This also talks about the applications of differential equations in the six exercises. NCERT Solutions for Class 12 Maths Chapter 10 Vector Equations. This chapter deals with the vector quantities, that is, the quantities with both magnitude and direction. The Vector algebra summarises the rules of addition of Class 8 Cbse Maths Marks Distribution vector quantities, and other important properties. To download Class 12 Maths NCERT Solutions and important questions with answers to help you revise complete Syllabus and score more marks in your exams visit myboat090 boatplans� Maths Class 12 NCERT Solutions Chapter 3 Exercises. Class 12 Maths Chapter 3 Exercise - 10 Questions with Solutions in PDF.

These ncert book chapter wise questions and answers are very helpful for CBSE board exam. Write down a unit vector in XY-plane making an angle of with the positive direction of axis.

Given points are P and Q. Scalar components of the vector are the coefficients of in , i. Now, draw BM perpendicular to axis. In by Triangle Law of Addition of vectors,. If then is it true that Justify your Class 8 Maths Ch 10 Ex 10.3 Cm answer. Either the vectors are collinear or form the sides of a triangle. Case I: Vectors are collinear. Let and. Case II: Vectors form a triangle. Here also by Triangle Law of vectors,. But [ Each side of a triangle is less than sum of the other two sides] is true only when vectors and are collinear vectors.

Since is a unit vector,. Squaring both sides,. Given: Vectors and. Let vector be the resultant vector of and. Required vector pf magnitude 5 units and parallel or collinear to resultant vector is. A unit vector parallel to the vector is. Given: Points A B and C 11, 3, 7. Let the point B divides AC in the ratio. Therefore, using section formula, Position vector of point B is. Comparing coefficients of both sides, we get.

Now vectors along the diagonals and of the parallelogram are. A unit vector along the given vector is. The given vector is in positive octant OXYZ and hence is acute. Now angle between and. Similarly, angle between and , ���. And angle between and , ���. Putting the values of in eq. But [ is acute and hence is positive] Therefore, required vectors are and.

We know that the cross-product of two vectors, is a vector perpendicular to both and. 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. Now squaring both sides of , we have,.

Putting , we have,. The value of is:. And this equation is true only for option B namely , since. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. Save my name, email, and website in this browser for the next time I comment. Download Now.

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