A vector has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense, if this respect to new system, has components p +1 and 1, then
p = 0
p = 1 or
p = -1
p = 1 or p = -1
If a, b, c are different real numbers and are position vectors of three non-collinear points, then
centroid of
is not really inclined to three vectors.
is a scalene triangle
Perpendicular from the origin to the plane of the triangle does not meet it at the centroid.
If are the position vectors of the vertices of an equilateral triangle, whose ortho centre is at the origin, then
Let be three non-zero vectors such that no two of these are collinear. If the vector + 2 is collinear with , then + 2 + 6 equals
λ (λ ≠ 0, a scalar)
0
Two vectors when act along the same line or along parallel lines are called
Collinear vectors
Coplanar vectors
Equal vectors
Position vectors
If = (2,1,-1), = (1,-1,0), =(5,-1,1) then unit vector parallel to but in opposite direction is
Let , , be three non-zero vectors such that no two of these are collinear. If the vector + 2 is collinear with , then + 2 + 6 equals
If the position vector of A with respect to O is , then the position vector of B with respect of O is
If the position vectors of the vertices of are , then the triangle ABC is
right angled and isosceles
right angled, but not isosceles
Isosceles but not right angled
equilateral
The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vectors is