Advertisements
Advertisements
Question
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
Options
`x/1 = y/2 = z/3`
`x/1 = y/1 = z/1`
`(x - 1)/1 = (y - 1)/2 = (z - 1)/3`
`(x - 1)/1 = (y - 2)/1 = (z - 3)/1`
Advertisements
Solution
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is `underlinebb((x - 1)/1 = (y - 2)/1 = (z - 3)/1)`.
Explanation:
∵ Line is passing through (1, 2, 3) and equally inclined to coordinate axes.
`\implies` Direction ratios are (1, 1, 1).
So equation of line will be `(x - 1)/1 = (y - 2)/1 = (z - 3)/1`
APPEARS IN
RELATED QUESTIONS
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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).
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).
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.
If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is
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
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
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
`1/5, 3/5, 4/5`
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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")`
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.
Find the direction cosine of a line which makes equal angle with coordinate axes.
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 ______.
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 ______.
Which identity must be satisfied by the direction cosines \[(l,m,n)\] of a line?
Any three numbers proportional to the direction cosines of a line are called its:
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
