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 line
`(x+2)/2=(2y-5)/3; z=-1`
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
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 the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
What are the direction cosines of Z-axis?
Write the distance of the point P (x, y, z) from XOY plane.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
Write direction cosines of a line parallel to z-axis.
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
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
The distance of the point P (a, b, c) from the x-axis 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) .
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
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 the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
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 ______.
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.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
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 ______.
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
