Advertisements
Advertisements
प्रश्न
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Advertisements
उत्तर
The given direction ratios are a = 3, b = – 1 , c = 3
If a, b, c are the direction ratios of a vector ten the direction cosines of the vector are
l = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c")`
c = `"c"/sqrt("a"^2 + "b"^2 + "c")`
∴ The required direction cosioes of the water are
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`(-1)/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(9 + 1 + 9)`
`(- 1)/sqrt(9 + 1 + 9)`
`3/sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1)/sqrt(9 + 1+ 9))`
`3/sqrt(9 + 1 + 9)`
`1/sqrt(19), (-1)/sqrt(19)`
= `3sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1) /sqrt(19), 3/sqrt(19))`
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 a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
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
2l + 2m − n = 0, mn + ln + lm = 0
Define direction cosines of a directed line.
What are the direction cosines of Y-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.
Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.
If a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2
The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.
If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
