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 direction cosines of a line which makes equal angles with the coordinate axes.
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
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 vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
What are the direction cosines of Y-axis?
Write the distance of the point (3, −5, 12) from X-axis?
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
Write direction cosines of a line parallel to z-axis.
A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
The angle between the two diagonals of a cube is
If a line makes angles α, β, γ, δ with four diagonals of a cube, then cos2 α + cos2 β + cos2γ + cos2 δ is equal to
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 and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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 angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.
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
O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
If a line has the direction ratio – 18, 12, – 4, then what are 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 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.
A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
