Advertisements
Advertisements
Question
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Solution
`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
RELATED QUESTIONS
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
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).
What are the direction cosines of Y-axis?
Write the distance of the point P (x, y, z) from XOY plane.
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
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`
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
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" + hat"j" + hat"k"`
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
If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.
If the directions cosines of a line are k,k,k, then ______.
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 ______.
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 ______.