Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Advertisements
उत्तर
`hat"j" = 0hat"i" + hat"j" + 0hat"k"`
The direction ratios of the vector `hat"j"` are (0, 1, 0)
The direction cosines of the vector `hat"j"` are
`0/sqrt(0^2 + 1^2 + 0^2), 1/sqrt(0^2 + 1^2 + 0^2), 0/sqrt(0^2 + 1^2 + 0^2)`
`0/1, 1/1, 0/1`
(0, 1, 0)
Direction ratios = (0, 1, 0)
Direction cosines = (0, 1, 0)
APPEARS IN
संबंधित प्रश्न
If a line has direction ratios 2, −1, −2, determine its direction cosines.
What are the direction cosines of Z-axis?
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.
For every point P (x, y, z) on the x-axis (except the origin),
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
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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
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 ______.
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
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.
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 ______.
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.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines 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 ______.
