हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

Choose the correct alternative: If the length of the perpendicular from the origin to the plane 2x + 3y + λz = 1, λ > 0 is 1/5, then the value of λ is

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

If the length of the perpendicular from the origin to the plane 2x + 3y + λz = 1, λ > 0 is `1/5, then the value of λ is

विकल्प

  • `2sqrt(3)`

  • `3sqrt(2)`

  • 0

  • 1

MCQ
Advertisements

उत्तर

`2sqrt(3)`

shaalaa.com
Different Forms of Equation of a Plane
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Applications of Vector Algebra - Exercise 6.10 [पृष्ठ २७८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 6 Applications of Vector Algebra
Exercise 6.10 | Q 25 | पृष्ठ २७८

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 non-parametric form of vector equation and cartesian equation of the plane passing through the point (1, − 2, 4) and perpendicular to the plane x + 2y − 3z = 11 and parallel to the line `(x + 7)/3 = (y + 3)/(-1) = z/1`


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


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


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 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:

If the line `(x  - )/3 = (y - 1)/(-5) = (x + 2)/2` lies in the plane x + 3y – αz + ß = 0 then (α + ß) is


Choose the correct alternative:

Distance from the origin to the plane 3x – 6y + 2z + 7 = 0 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 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 `(x - 2)/3 = (y + 1)/(-2) = (z + 3)/(-1)` lie on the plane px – qy + z = 5, for p, q ∈ R. The shortest distance of the plane from the origin is ______.


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×