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
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
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`
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
What are the direction cosines of X-axis?
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
For every point P (x, y, z) on the x-axis (except the origin),
A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
The angle between the two diagonals of a cube is
The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are _______.
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
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 ______.
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
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.
Find the direction cosine of a line which makes equal angle with coordinate axes.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
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 ______.
A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
