Advertisements
Advertisements
Question
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Advertisements
Solution 1
A-line makes 90° and 135°, 45°with x, y and z axes, respectively.
Therefore, Direction cosines of the line are cos 90°, cos135°, and cos45°
⇒ Direction cosines of the line are 0, `-(1)/sqrt(2),(1)/sqrt(2)`
Solution 2
Let the direction cosines of the line be l, m and n.
a = 90°, b = 135°, c = 45°
Now,
l = cos a = cos 90° = 0
m = cos b = cos 135° = `-1/sqrt2`
n = cos c = cos 45° = `1/sqrt2`
direction cosines of a line = `0, -1/sqrt2, 1/sqrt2`
RELATED QUESTIONS
Find the direction cosines of a line which makes equal angles with the coordinate axes.
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 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).
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
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).
If the coordinates of the points A, B, C, D are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.
Find the angle between the lines whose direction cosines are given by the equations
2l − m + 2n = 0 and mn + nl + lm = 0
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
What are the direction cosines of X-axis?
Write the distance of the point (3, −5, 12) from X-axis?
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
For every point P (x, y, z) on the xy-plane,
For every point P (x, y, z) on the x-axis (except the origin),
The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are _______.
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
`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
`3hat"i" + hat"j" + hat"k"`
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
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
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 ______.
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.
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
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.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
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 ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
A directed line makes angles \[\alpha\], \[\beta\], and \[\gamma\] with the positive x-, y-, and z-axes respectively. What are these angles called?
