If the projections of `bar(PQ)` on the axes are 2, -2, 1 then the length PQ =

If the projections of the line segment bar(PQ) on the axes are 3, 4, 12 then the length of bar(PQ) is

A line with positive direction cosines passes through the point P(2,-1,2) and makes equal angles with the coordinate axes. If the line meets the plane 2x+y+z=9 at the point Q, then the length PQ equals.

If P=(3,-4,1), Q=(4,0,2) then find the projection of bar(PQ) on the plane 2x-y+2z=3 .

P=(0,1,0),Q=(0,0,1) then projection of bar(PQ) on the plane x+y+z=3 is

The bar is subjected to equal and opposite forces as shown in the figure PQ is plane making angle with the cross-section of the bar. If the area of cross-section be 'a', then what is the tensile stress on PQ ?

If the projection of a line of length d on the coordinate axes are d_(1),d_(2),d_(3) " respectively then, prove that " d^(2) = (d_(1)^(2)+d_(2)^(2)+d_(3)^(2))/2

A line is drawn through the point (1,2) to meet the co-ordinate axes at P and Q such that it forms a Delta^(1e) OPQ, where O is the origin. If the area of the Delta OPQ, is least, then the slope of the line PQ is

If P, Q are the points of trisection of A(1, -2), B(-5, 6) then PQ =

The position vector of the points P, Q, R, S are bar(i)+bar(j)+bar(k), 2bar(i)+5bar(j), 3bar(i)+2bar(j)-3bar(k) and bar(i)-6bar(j)-bar(k) respectively. Prove that bar(PQ) and bar(RS) are parallel and find the ratio of their lengths.

Assertion (A) : P(3,4,5), Q(-1,7,9) are two given points, length of projection of PQ on xyplane is 5 units Reason ( R ): The projection of (x_(1),y_(1),z_(1)) " on XY PLANE is (x_(1),y_(1),0)