Advertisements
Advertisements
प्रश्न
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
पर्याय
`(2x)/sqrt(3) = y/2 = z/0`
`(2x)/sqrt(3) = (2y)/1 = z/0`
2x = `(2y)/sqrt(3) = z/1`
`(2x)/sqrt(3) = (2y)/1 = z/1`
Advertisements
उत्तर
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is `underlinebb((2x)/sqrt(3) = (2y)/1 = z/0)`.
Explanation:
Here, direction cosines of the line are
l = cos 30°, m = cos 60°, n = cos 90°
l = `sqrt(3)/2`, m = `1/2`, n = 0
Here, line passes through the point (0, 0, 0).
So, the required equation of line is
`(x - 0)/(sqrt(3)/2) = (y - 0)/(1/2) = (z - 0)/0`
`\implies (2x)/sqrt(3) = (2y)/1 = z/0`
APPEARS IN
संबंधित प्रश्न
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
What are the direction cosines of Z-axis?
Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
For every point P (x, y, z) on the xy-plane,
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`, find the magnitude and direction cosines of `3vec"a"- 2vec"b"+ 5vec"c"`
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.
The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
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.
A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.
If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c 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.
