Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
2
1
–1
–2
Advertisements
उत्तर
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 2.
Explanation:
Let P divides the line segment in the ratio of λ : 1
x - coordinate of the point P may be expressed as x = `(6lambda + 3)/(lambda + 1)` giving `(6lambda + 3)/(lambda + 1)` = 5
So that λ = 2.
Thus y-coordinate of P is `(2lambda + 2)/(lambda + 1)` = 2.
APPEARS IN
संबंधित प्रश्न
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`
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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`
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 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).
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
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 Y-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
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 xy-plane,
If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
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"`
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.
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 ______.
The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
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
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.
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.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
A directed line makes angles \[\alpha\], \[\beta\], and \[\gamma\] with the positive x-, y-, and z-axes respectively. What are these angles called?
Which identity must be satisfied by the direction cosines \[(l,m,n)\] of a line?
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
For direction ratios \[(a,b,c)\], which set can represent the corresponding direction cosines when the direction of the line is chosen?
