Advertisements
Advertisements
प्रश्न
Find the non-parametric form of vector equation and Cartesian equations of the plane `vec"r" = (6hat"i" - hat"j" + hat"k") + "s"(-hat"i" + 2hat"j" + hat"k") + "t"(-5hat"i" - 4hat"j" - 5hat"k")`
Advertisements
उत्तर
`vec"a" = 6hat"i" - hat"j" + hat"k"`
`vec"b" = -hat"i" + 2hat"j" + hat"k"`
`vec"c" = -5hat"i" - 4hat"j" - 5hat"k"`
`vec"b" xx vec"c" = |(hat"i", hat"j", hat"k"),(-1, 2, 1),(-5, -4, -5)|`
= `hat"i"(- 10 + 4) - hat"j"(5 + 5) + hat"k"(4 + 10)`
= `-6hat"i" - 10hat"j" + 14hat"k"`
= `-2(3hat"i" + 5hat"j" - 7hat"k")`
Non-parametric vector equation:
`(vec"r" - vec"a")*(vec"b" xx vec"c") = vec0`
`[vec"r" - (6hat"i" - hat"j" + hat"k")]*(3hat"i" + 5hat"j" - 7hat"k") = vec0`
`vec"r"*(3hat"i" + 5hat"j" - 7hat"k")` = 18 – 5 – 7 = 6
`vec"r"*(3hat"i" + 5hat"j" - 7hat"k")` = 6
Cartesian equation:
3x + 5y – 7z = 6
3x + 5y – 7z – 6 = 0
APPEARS IN
संबंधित प्रश्न
Find a parametric form of vector equation of a plane which is at a distance of 7 units from t the origin having 3, – 4, 5 as direction ratios of a normal to it
Find the intercepts cut off by the plane `vec"r"*(6hat"i" + 45hat"j" - 3hat"k")` = 12 on the coordinate axes
If a plane meets the co-ordinate axes at A, B, C such that the centroid of the triangle ABC is the point (u, v, w), find the equation of the plane
Find the parametric form of vector equation, and Cartesian equations of the plane passing through the points (2, 2, 1), (9, 3, 6) and perpendicular to the plane 2x + 6y + 6z = 9
If the straight lines `(x - 1)/2 = (y + 1)/lambda = z/2` and `(x + 1)/5 = (y + 1)/2 = z/lambda` are coplanar, find λ and equations of the planes containing these two lines
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:
The angle between the lines `(x - 2)/3 = (y + 1)/(-2)`, z = 2 ad `(x - 1)/1 = (2y + 3)/3 = (z + 5)/2` is
Choose the correct alternative:
The angle between the line `vec"r" = (hat"i" + 2hat"j" - 3hat"k") + "t"(2hat"i" + hat"j" - 2hat"k")` and the plane `vec"r"(hat"i" + hat"j") + 4` = 0 is
Choose the correct alternative:
If the planes `vec"r"(2hat"i" - lambdahat"j" + hatk")` = and `vec"r"(4hat"i" + hat"j" - muhat"k")` = 5 are parallel, then the value of λ and µ 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 equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is ______.
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 point in which the join of (–9, 4, 5) and (11, 0, –1) is met by the perpendicular from the origin 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 ______.
