The Number Of Vectors Of Unit Length Perpendicular To The Vectors  

The values of x for which the angle between the vectors  is acute, and the angle between the vector  and the axis of ordinates is obtuse, are

The value of x for which the angle between  and  is obtuse and the angle between  and the z-axis is acute and less than π/6, are  

If  are two unit vectors such that , then the angle between , is 

, then the angle between  

If  are unit vectors and θ is the acute angle between them, then  is a unit vector for

For any vector   

 is equal to 

A unit vector perpendicular to the plane of  and  is 

A unit vector making an obtuse angle with x-axis and perpendicular to the plane containing the points  also makes an obtuse angle with