Advertisements
Advertisements
Question
What are the direction cosines of X-axis?
Advertisements
Solution
\[\text { The x - axis makes angles 0°, 90° and 90° with x, y and z axes, respectively } . \]
\[\text{ Therefore, the direction cosines of x - axis are cos 0°, cos 90° , cos 90° , i . e} . 1, 0, 0 .\]
APPEARS IN
RELATED QUESTIONS
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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 direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (−1, −2, 1) and (1, 2, 5).
Find the angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0
Find the angle between the lines whose direction cosines are given by the equations
2l − m + 2n = 0 and mn + nl + lm = 0
What are the direction cosines of Z-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
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
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
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 _______.
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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
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 `vec"a", vec"b", vec"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
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.
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 the directions cosines of a line are k,k,k, then ______.
The line `vec"r" = 2hat"i" - 3hat"j" - hat"k" + lambda(hat"i" - hat"j" + 2hat"k")` lies in the plane `vec"r".(3hat"i" + hat"j" - hat"k") + 2` = 0.
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
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 ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
Which identity must be satisfied by the direction cosines \[(l,m,n)\] of a line?
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
In the relation between direction ratios and direction cosines, what does the sign \[\pm\] in \[l=\pm\frac{a}{\sqrt{a^2+b^2+c^2}}\] depend on?
A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?
