मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता १२

Consider the vectors abcda→,b→,c→,d→ such that abcd(a→×b→)×(c→×d→)=0→. Let P1 and P2 be the planes determined by the pairs of vectors aba→,b→ and , vec′→c, vecd respectively. Then the - Mathematics

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 45°

  • 60°

  • 90°

MCQ

उत्तर

shaalaa.com
Different Forms of Equation of a Plane
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Applications of Vector Algebra - Exercise 6.10 [पृष्ठ २७७]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 6 Applications of Vector Algebra
Exercise 6.10 | Q 12 | पृष्ठ २७७

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 vector and Cartesian equation of the plane passing through the point with position vector `2hat"i" + 6hat"j" + 3hat"k"` and normal to the vector `hat"i" + 3hat"j" + 5hat"k"`


A plane passes through the point (− 1, 1, 2) and the normal to the plane of magnitude `3sqrt(3)` makes equal acute angles with the coordinate axes. Find the equation of the plane


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


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")`


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


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", 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:

If the volume of the parallelepiped with `vec"a" xx vec"b", vec"b" xx vec"c", vec"c" xx vec"a"` as coterminous edges is 8 cubic units, then the volume of the parallelepiped with `(vec"a" xx vec"b") xx (vec"b" xx vec"c"), (vec"b" xx vec"c") xx (vec"c" xx vec"a")` and `(vec"c" xx vec"a") xx (vec"a" xx vec"b")` as coterminous edges is


Choose the correct alternative:

If `vec"a" = 2hat"i" + 3hat"j" - hat"k", vec"b" = hat"i" + 2hat"j" - 5hat"k", vec"c" = 3hat"i" + 5hat"j" - hat"k"`, then a vector perpendicular to `vec"a"` and lies in the plane containing `vec"b"` and `vec"c"` 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


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


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 point in which the join of (–9, 4, 5) and (11, 0, –1) is met by the perpendicular from the origin is ______.


A point moves in such a way that sum of squares of its distances from the co-ordinate axis is 36, then distance of then given point from origin are ______.


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×