Advertisements
Advertisements
Question
Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
Solution
Passing through point (2, 1, 3) .........given
(x, y, z) = (2, 1, 3)
Perpendicular to the lines.
`(x-1)/1 = (y-2)/2 =(z-3)/3` and `X/-3 = Y/2 = Z/5`
Let `veca = hati +2hatj + 3k`
`barb = -3hatj + 2hatj + 3k`
`baraxxhatb = |(hati hatj hatk),(1 2 3),(-3 2 5)|`
`=hati(10-6)-j(5+9)+hatk(2+6)`
`= 4hati - 14hatj + 8k`
D.r.’s of required line : 4, - 14,8
i.e, 2,-7,4
Required equation of line `(x-2)/2 = (y-1)/-7 = (z - 3)/4`
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
Find the angle between the lines whose direction cosines are given by the equations
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are _______.
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.
If a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2
If the directions cosines of a line are k,k,k, then ______.
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If the equation of a line is x = ay + b, z = cy + d, then find the direction ratios of the line and a point on the line.
Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.
