Vectors Test - ...

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The position vector of a point say and its magnitude is

Reason (R): If then coefficient of are called the direction ratios of vector

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A) : The area of parallelogram with diagonals

Reason (R): If represent the adjacent sides of a triangle, then the area of triangle can be obtained by evaluating

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The direction of cosines of vector

Reason (R): A vector having zero magnitude and arbitrary direction is called ‘zero vector’ or ‘null vector’.

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The position of a particle in a rectangular coordinate system is (3, 2, 5). Then its position vector be

Reason (R): The displacement vector of the particle that moves from point P(2, 3, 5) to point Q(3, 4, 5) is

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The vectors which can undergo parallel displacement without changing its magnitude and direction are called free vectors.

Reason (R):

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): For any two vectors we always have

Reason (R): The given inequality holds trivially when either in such a case

Then consider

So, let us check it for

For cos θ ≤ 1, we have :

or

or

If   are any two vectors, then

The angle between the vectors is:   is :

If    are two vectors, such that   , then  = ……​

The projection of the vector    on the vector is:​

The angle between two non-zero vectors   is given by

If | a | = 2, | b | = 5 and | a ×b | = 8, thencan be equal to

If  are unit vectors along X-axis, Y-axis and Z-axis respectively, then

The area of triangle whose adjacent sides are is :

The value of   is:

The area of parallelogram whose sides areis:​