Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
Advertisements
उत्तर
The direction ratios of the vector `5hat"i" - 3hat"j" - 48hat"k"` are (5, – 3, – 48)
The direction cosines of the vector `5hat"i" - 3hat"j" - 48hat"k"` are
`5/sqrt(5^2 + (-3)^2 + (-48)^2), (-3)/sqrt(5^2 + (-3)^2 + (-48)^2), (-48)/sqrt(5^2 + (-3)^2 + (-48)^2)`
`5/sqrt(25 + 9 + 2304), (-3)/sqrt(25 + 9 + 2304), (-48)/sqrt(25 + 9 + 2304)`
`(5/sqrt(2338), (-3)/sqrt(2338), (-4)/sqrt(2338))`
Direction ratios = (5, – 3, – 48)
Direction cosies = `(5/sqrt(2338), (-3)/sqrt(2338), (-4)/sqrt(2338))`
APPEARS IN
संबंधित प्रश्न
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 l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
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.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
Find the angle between the lines whose direction cosines are given by the equations
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
Write the distance of the point P (x, y, z) from XOY plane.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
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
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
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
If the directions cosines of a line are k,k,k, then ______.
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.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
