If are non-zero vectors such that then
Assertion : Least value of is
Reason (R): The expression is least when magnitude of is

Statement- 1: If and and , then there exist real numbers , such that
Statement- 2: are four vectors in a 3 - dimensional space. If are non-coplanar, then there exist real numbers such that

Statement- :If are non-collinear points. Then every point in the plane of , can be expressed in the form
Statement- :The condition for coplanarity of four points is that there exists scalars not all zeros such that   where .

Assertion (A): The number of vectors of unit length and perpendicular to both the vectors. and is zero Reason
(R): and are two non-zero and non-parallel vectors it is true that is perpendicular to the plane containing and

The value of for which the straight lines and are coplanar is

For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.

The position vector of the centre of the circle

Let where are three noncoplanar vectors. If is perpendicular to , then minimum value of

Which of the following represents Westrosol?

Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?

For the preparation of chloroethane

 Which of the following statements is wrong about the reaction?

In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?

The final product (X) in the following reaction is:

Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis

Two adjacent sides of a parallelogram are given by and . The side is rotated by an acute angle in the plane of parallelogram so that becomes AD’. If makes a right angle with the side AB then the cosine of angle is given by

If then