हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

Find the intercepts cut off by the plane rijkr→⋅(6i^+45j^-3k^) = 12 on the coordinate axes - Mathematics

Advertisements
Advertisements

प्रश्न

Find the intercepts cut off by the plane `vec"r"*(6hat"i" + 45hat"j" - 3hat"k")` = 12 on the coordinate axes

योग

उत्तर

`vec"r"*(6hat"i" + 45hat"j" - 3hat"k")` = 12

`(hat"i" + yhat"j" + zhat"k")*(6hat"i" + 4hat"j" - 3hat"k")` = 2

`6x + 4y - 3z` = 12

`x/2 + y/3 + z/(-4)` = 1  ......(÷ 12)

x-intercept = 2

y-intercept = 3

z-intercept = – 4

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 6.6 [पृष्ठ २५९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 6 Applications of Vector Algebra
Exercise 6.6 | Q 5 | पृष्ठ २५९

संबंधित प्रश्न

Find the direction cosines of the normal to the plane 12x + 3y – 4z = 65. Also find the non-parametric form of vector equation of a plane and the length of the perpendicular to the plane from the origin


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


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 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 passing through the points (2, 2, 1), (9, 3, 6) and perpendicular to the plane 2x + 6y + 6z = 9


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 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)/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:

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:

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:

Distance from the origin to the plane 3x – 6y + 2z + 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 `(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 ______.


A plane P contains the line x + 2y + 3z + 1 = 0 = x – y – z – 6, and is perpendicular to the plane –2x + y + z + 8 = 0. Then which of the following points lies on P?


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×