Prove that 1,1,1 cannot be direction cosines of a straight line.

Define direction cosines of a directed line.

The direction cosines of the line 6x-2=3y+1=2z-2 are

The direction cosines of the line 6x-2=3y+1=2z-2 are

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are 1/(sqrt(3)),1/(sqrt(3)),1/(sqrt(3)) .

Write the direction cosines of a line parallel to z-axis.

If the direction cosines of a line are lt k, k, kgt then

Prove that the lines whose direction cosines are given by the equations l+m+n=0 and 3lm-5mn+2nl=0 are mutually perpendicular.

can -1/(2sqrt(2))-1/sqrt(2),-1/sqrt(3) be the direction cosines of any directed line? Justify your answer.

If l_(1), m_(1), n_(1) and l_(2),m_(2),n_(2) are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

If l_(1), m_(1), n_(1) and l_(2),m_(2),n_(2) are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .