Advertisements
Advertisements
प्रश्न
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
पर्याय
`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
उत्तर
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
संबंधित प्रश्न
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
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.
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) 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).
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
Define direction cosines of a directed line.
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.
Find the distance of the point (2, 3, 4) from the x-axis.
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
The angle between the two diagonals of a cube is
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
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.
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.
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 ______.
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 ______.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
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 ______.
