Vector Algebra ...

If line     is parallel to the plane , then the value of m is  

Given      , then  

simplifies to  

Let   be a vector perpendicular to   , where   then (ℓ+m+n) is equal to  

If    are three non-coplaner non-zero vectors and   is any vector in space, then      is equal to

If a, b, c are pth, qth, rth terms of an H.P and  

If the unit vectors   are inclined at an angle 2 θ and  , then for  θ ∈ [0, π], θmay lie in the interval  

Consider a tetrahedron with faces f₁ , f₂ , f ₃ , f₄   Let   ​be the vectors whose magnitudes are respectively equalt to the areas of   f₁ , f₂ , f₃ , f₄  and  whose directions are perpendicular to these faces in the outward direction. Then

Let    be non-coplaner unit vectors equally inclined to one another at an acute angle  θ. Then  in terms of   θis equalt to  

Let    and    . If the vector     lies in the plane of   , then x equals  

Images of the point P with position vector     in the line whose vector equation is  has the position vector

Let    be such that   . If the projection   is equal to that of    are  perpendicular  to each other, then   equals.

Let    and   . If    is a unit vector such that    then   is equal to  

Equation of a line which passes through a point with position vector   , parallel to the plane    and perpendicular to the line