Advertisements
Advertisements
Question
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Advertisements
Solution
The equation of the given line can be rewritten as:
`(x+3)/0=(y−4)/3=(z−2)/(−1)`
Thus, the given line has direction ratios proportional to 0, 3, −1.
APPEARS IN
RELATED QUESTIONS
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1
If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
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 vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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 distance of the point P (x, y, z) from XOY plane.
For every point P (x, y, z) on the xy-plane,
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
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" - 4hat"j" + 8hat"k"`
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.
A line makes equal angles with co-ordinate axis. Direction cosines of this line 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 ______.
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 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 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 ______.
