Show that the perpendicular distance from a point `A(veca)` to the line `vecr=vecb+tvecc is |vecb+((veca.vecb).vecc)/c^2 vecc-veca|`

Show that the perpendicular distance of any point veca from the line vecr=vecb+t vecc is (|(vecb-veca)xxvecc)|/(|vecc|)

The distance of the point A(veca) from the line vecr=vecb+tvecc is (A) |(veca-vecb)xxvecc| (B) (|(veca-vecb)xxvecc|)/(|(veca-vecb)|) (C) (|(veca-vecb)xxvecc|)/(|vecc|) (D) (|vecaxx(vecb-vecc)|)/(|veca|)

A line l is passing through the point vecb and is parallel to vector vecc . Determine the distance of point A( veca) from the line l in from |vecb-veca+((veca-vecb)vecc)/(|vecc|^(2))vecc|or (|(vecb-veca)xxvecc|)/(|vecc|)

Show that the plane through the points veca,vecb,vecc has the equation [vecr vecb vecc]+[vecr vecc veca]+[vecr veca vecb]=[veca vecb vecc]

If veca and vecb be two non collinear vectors such that veca=vecc+vecd , where vecc is parallel to vecb and vecd is perpendicular to vecb obtain expression for vecc and vecd in terms of veca and vecb as: vecd= veca- ((veca.vecb)vecb)/b^2,vecc= ((veca.vecb)vecb)/b^2

If veca,vecb and vecc are three mutually perpendicular unit vectors then (vecr.veca)veca+(vecr.vecb)vecb+(vecr.vecc)vecc= (A) ([veca vecb vecc]vecr)/2 (B) vecr (C) 2[veca vecb vecc] (D) none of these

Show that the points whose position vectors are veca,vecb,vecc,vecd will be coplanar if [veca vecb vecc]-[veca vecb vecd]+[veca vecc vecd]-[vecb vecc vecd]=0

If veca,vecb,vecc are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is (A) veca+vecb+vecc (B) veca/|veca|+vecb/|vecb|+vec/|vecc| (C) veca/|veca|^2+vecb/|vecb|^2+vecc/|vecc|^2 (D) |veca|veca-|vecb|vecb+|vecc|vecc

If veca, vecb,vecc are unit vectors such that veca is perpendicular to the plane of vecb, vecc and the angle between vecb,vecc is pi/3 , then |veca+vecb+vecc|=

If vecb and vecc are any two orthogonal unit vectors and veca is any vector, then (veca.vecb)vecb + (veca.vecc)vecc + (veca.(vecb xx vecc))/|vecb xx vecc|^(2) (vecb xx vecc) =