A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) wit...

The direction ratios of a line passing through the points A(1,2,6) and B(-4,5,0) are

Line L_(1) is parallel to vector vec alpha=-3hat i+2hat j+4hat k and passes through a point A(7,6,2) and line L_(2) is parallel vector vec beta=2hat i+hat j+3hat k and point B(5,3,4). Now a line L_(3) parallel to a vector vec r=2hat i-2hat j-hat k intersects the lines L_(1) and L_(2) at points C and D, respectively, then find |vec CD|

Line L_(1) is parallel to vector vec(alpha) = - 3hati + 2hatj+ 4hatk and passes through a point A(7, 6, 2) and line L_(2) is parallel to a vector vec(beta) = 2hati + 2hatj + 3hatk and passes through a point B(5,3,4). Now a line L_(3) parallel to a vector vec(r) = 2hati - 2hatj - hatk intersects the line L_(1) and L_(2) at point C and D respectively, Find |vec(CD)| .

A line L has a slope of -2 and passes through the point (r,,-3). A second line,K is perpendicular to L at (a,b) and passes through the point (6,r). Find a in terms of r.

In the xy plane,the line L_(1) passes through the point (1,1) and the line L_(2) passes through the point (-1,1). If the difference of the slopes of the lines is 2. Then the locus of the point of intersection of the lines L_(1) and L_(2) is

Find the slope of the following lines. (i) Line parallel to X-axis . (ii) Line passing through the points A(-2,-3) and B(2,4) (iii) Line passing through the points P (3,2) and Q(4,1) . (iv) Line passing through the points A(-3,5) and B (4,-1). (v) Line passing through points C(3,5) and D(-2,-3) . (vi) Line passing through the points A (6,-2) and B (-3,4) .

The line l_(1) passing through the point (1,1) and the l_(2), passes through the point (-1,1) If the difference of the slope of lines is 2. Find the locus of the point of intersection of the l_(1) and l_(2)

Suppose that the points (h,k) , (1,2) and (-3,4) lie on the line L_(1) . If a line L_(2) passing through the points (h,k) and (4,3) is perpendicular to L_(1) , then k//h equals

Direction cosines of the line passing through the points A(-4, 2, 3) and B(1, 3, -2) are