Advertisements
Advertisements
प्रश्न
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Advertisements
उत्तर
P(4,3,-5) & Q(-2,1,-8)
equation of line
`(x-4)/(-2-4) = (y-3)/(1-3) = (z+5)/(-8-(-5)) = lambda`
`(x-4)/-6 = (y-3)/-2 = (z+5)/-3 = lambda`
`therefore "drs of line is" 6,2,3`
⇒ `dcs = 6/(sqrt(6^2+2^2+3^2)) , 2/(sqrt(6^2+2^2+3^2)) , 3/(sqrt(6^2+2^2+3^2))`
= `6/7 , 2/7 , 3/7`
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`
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.
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
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
What are the direction cosines of X-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
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 coordinates of the projection of the point P (2, −3, 5) on Y-axis.
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
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"`
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.
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 ______.
A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.
If the directions cosines of a line are k,k,k, then ______.
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 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 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 ______.
