Vectors

If are non-coplanar unit vectors such that then the angle between a and b is

if , and are three non-coplanar vectors, then equal to

Given below are two statements:
Statement I: Three points with position vectors are collinear if there exists scalars x,y,z not all zero such that , where x+y+z=0.
Statement II: Scalar product and vector product are both commutative.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: The vector equation of line passing through two points with position vector and is
Statement II: The vector equation of a straight line passing through a fixed point with position vector and parallel to a given vector is where λ is scalar.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: Let , , be three vectors. Then the scalar is called the scalar product of and is denoted by .
Statement II: is vector which is ⊥ to and both.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Which of the following is not correct?
(A) Sum of the vectors directed from the vertices to the mid-points of opposite side of a triangle is zero.
(B) Medians of a triangle are not concurrent.
(C) The diagonals of a quadrilateral bisect each other iff it is a parallelogram.
(D) Vectors having the different terminal point are called co-terminus vectors.
Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If dot product and cross product of are zero, it implies that one of the vector must be null vector
Reason R: Null vector is a vector with a zero magnitude.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following is true :
A. Two vectors are said to be identical if their difference is zero.
B. Velocity is not a vector quantity.
C. Projection of one vector on another is not an application of dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
Choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: The angle between the vectors and is
Statement II: The vector is coplanar with and
In the light of the above statements, choose the correct answer from the options given below:

If the unit vectors and are inclined at an angle 2\theta such that and , then \theta lies in the interval.

Each of the angle between vectors and is equal to 60°. If then the modulus of is

If are such that is perpendicular to then determine the value of ?

Match List-I and List-II

LIST I		LIST II
A.		I.	45°
B.		II.	30°
C.		III.	90°
D.		IV.	60°

Choose the correct answer from the options given below: