For three vectors which of the following expressions is not equal to any of the remaining three?
So, expression in options (i) and (ii) are equal.
Since the positions of dot and cross can be interchanged in scalar triple product. Therefore,
So, expression in options (i) and (iv) are equal.
Hence, expression in (iii) is note equal to the remaining three.
The three concurrent edges of a parallelopiped represent the vectors such that Then, the volume of the parallelopiped whose three concurrent edges are the three diagonals of three faces of the given parallelepiped is
Which of the following expressions are meaningful?
are linearly dependent vectors and , then
The volume of the tetrahedron whose vertices are the points with position vectors and is 11 cubic units if the value of λ is
If a vector is expressed as the sum of two vectors along and perpendicular to a given vector
are two given vectors. On these vectors as adjacent sides a parallelogram is constructed. The vector which is the altitude of the parallelogram and which is perpendicular to is not equal to
Let be a unit vector and a non-zero vector not parallel to . The angles of the triangle, two of whose sides are represented by
Three vectors taken two at a time form three planes. The three unit vectors drawn perpendicular to three planes form a parallelopiped of volume