Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If the line `(x - )/3 = (y - 1)/(-5) = (x + 2)/2` lies in the plane x + 3y – αz + ß = 0 then (α + ß) is
पर्याय
(– 5, 5)
(– 6, 7)
(5, – 5)
(6, – 7)
Advertisements
उत्तर
(– 6, 7)
APPEARS IN
संबंधित प्रश्न
Find the non-parametric form of vector equation and Cartesian equation of the plane passing through the point (2, 3, 6) and parallel to thestraight lines `(x - 1)/2 = (y + 1)/3 = (x - 3)/1` and `(x + 3)/2 = (y - 3)/(-5) = (z + 1)/(-3)`
Find the parametric form of vector equation, and Cartesian equations of the plane containing the line `vec"r" = (hat"i" - hat"j" + 3hat"k") + "t"(2hat"i" - hat"j" + 4hat"k")` and perpendicular to plane `vec"r"*(hat"i" + 2hat"j" + hat"k")` = 8
Show that the straight lines `vec"r" = (5hat"i" + 7hat"j" - 3hat"k") + "s"(4hat"i" + 4hat"j" - 5hat"k")` and `vec"r"(8hat"i" + 4hat"j" + 5hat"k") + "t"(7hat"i" + hat"j" + 3hat"k")` are coplanar. Find the vector equation of the plane in which they lie
Show that the lines `(x - 2)/1 = (y - 3)/1 = (z - 4)/3` and `(x - 1)/(-3) = (y - 4)/2 = (z - 5)/1` are coplanar. Also, find the plane containing these lines
If the straight lines `(x - 1)/1 - (y - 2)/2 = (z - 3)/"m"^2` and `(x - 3)/5 = (y - 2)/"m"^2 = (z - 1)/2` are coplanar, find the distinct real values of m
Choose the correct alternative:
If `vec"a", vec"b", vec"c"` are three unit vectors such that `vec"a"` is perpendicular to `vec"b"`, and is parallel to `vec"c"` then `vec"a" xx (vec"b" xx vec"c")` is equal to
Choose the correct alternative:
The volume of the parallelepiped with its edges represented by the vectors `hat"i" + hat"j", hat"i" + 2hat"j", hat"i" + hat"j" + pihat"k"` is
Choose the correct alternative:
If `vec"a"` and `vec"b"` are unit vectors such that `[vec"a", vec"b", vec"a" xx vec"b"] = 1/4`, are unit vectors such that `vec"a"` nad `vec"b"` is
Choose the correct alternative:
If `vec"a", vec"b", vec"c"` are three non-coplanar vectors such that `vec"a" xx (vec"b" xx vec"c") = (vec"b" + vec"c")/sqrt(2)` then the angle between `vec"a"` and `vec"b"` is
Choose the correct alternative:
Consider the vectors `vec"a", vec"b", vec"c", vec"d"` such that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`. Let P1 and P2 be the planes determined by the pairs of vectors `vec"a", vec"b"` and `vec'c", vec"d"` respectively. Then the angle between P1 and P2 is
Choose the correct alternative:
The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0 is
Choose the correct alternative:
If the distance of the point (1, 1, 1) from the origin is half of its distance from the plane x + y + z + k = 0, then the values of k are
Let d be the distance between the foot of perpendiculars of the points P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d2 is equal to ______.
The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point ______.
The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is ______.
The point in which the join of (–9, 4, 5) and (11, 0, –1) is met by the perpendicular from the origin is ______.
Consider a plane 2x + y – 3z = 5 and the point P(–1, 3, 2). A line L has the equation `(x - 2)/3 = (y - 1)/2 = (z - 3)/4`. The co-ordinates of a point Q of the line L such that `vec(PQ)` is parallel to the given plane are (α, β, γ), then the product βγ is ______.
Let (λ, 2, 1) be a point on the plane which passes through the point (4, –2, 2). If the plane is perpendicular to the line joining the points (–2, –21, 29) and (–1, –16, 23), then `(λ/11)^2 - (4λ)/11 - 4` is equal to ______.
