Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, x = ay + b, z = cy + d
`\implies (x - b)/a` = y and `(z - d)/c` = y
`\implies (x - b)/a = y/1 = (z - d)/c`
∴ Direction ratios of given line is < a, 1, c >.
And a point on the given line is (b, 0, d).
APPEARS IN
संबंधित प्रश्न
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, −4), (−1, 1, 2) and (−5, −5, −2).
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.
For every point P (x, y, z) on the xy-plane,
The distance of the point P (a, b, c) from the x-axis is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are
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 _______.
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
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"`
Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is
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 ______.
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
The d.c's of a line whose direction ratios are 2, 3, –6, 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 ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
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 ______.
