Advertisements
Advertisements
प्रश्न
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
Advertisements
उत्तर
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are `2/3, 2/3, (-1)/3`.
Explanation:
Let `vec"a" = 2hat"i" + 2hat"j" - hat"k"`
Direction ratios of `vec"a"` are 2, 2, – 1
So, the direction cosines are `2/sqrt(4 + 4 + 1)`
`2/sqrt(4 + 4 + 1)`
`-1/sqrt(4 + 4 + 1)`
⇒ `2/3, 2/3, (-1)/3`
APPEARS IN
संबंधित प्रश्न
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1
Which of the following represents direction cosines of the line :
(a)`0,1/sqrt2,1/2`
(b)`0,-sqrt3/2,1/sqrt2`
(c)`0,sqrt3/2,1/2`
(d)`1/2,1/2,1/2`
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.
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1.
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
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
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
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
What are the direction cosines of Y-axis?
Write the distance of the point (3, −5, 12) from X-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.
Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.
Write the distance of the point P (x, y, z) from XOY plane.
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
The distance of the point P (a, b, c) from the x-axis is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
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
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
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
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
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"`
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.
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 ______.
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 d.c's of a line whose direction ratios are 2, 3, –6, are ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
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 ______.
