Advertisements
Advertisements
प्रश्न
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
Advertisements
उत्तर
We have, `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`
The equation of line AB can be rewritten as `(x - 1/2)/6 = (y - (-2))/2 = (z - 3)/3`
Thus, direction ratios of the line parallel to AB are proportional to 6, 2, 3.
Hence, the direction cosines of the line parallel to AB are proportional to `6/sqrt(6^2 + 2^2 + 3^2), 2/sqrt(6^2 + 2^2 + 3^2), 3/sqrt(6^2 + 2^2 + 3^2)`
or `6/sqrt(49), 2/sqrt(49), 3/sqrt(49)`
or `6/7, 2/7, 3/7`
APPEARS IN
संबंधित प्रश्न
Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
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.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
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
2l − m + 2n = 0 and mn + nl + lm = 0
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
Write direction cosines of a line parallel to z-axis.
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
For every point P (x, y, z) on the xy-plane,
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
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
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
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 (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c
If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.
If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.
O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
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 has the direction ratio – 18, 12, – 4, then what are its direction cosine.
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 ______.
A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.
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 ______.
