Home
Class 12
MATHS
Show that x(1) hati+y(1) hatj+ z1hatk, x...

Show that `x_(1) hati+y_(1) hatj+ z_1hatk, x_2hati+y_2hatj+z_2hatk and x_3hati+y_3hatj+z_3hatk` are non-coplnar if `|x_1| gt |y_1|+ |z_1|`, `|y_2| gt |x_2|+|z_2| and |z_3|gt |x_3| + |y_3|`.

A

perpendicular

B

collinear

C

coplanar

D

non coplanar

Text Solution

Verified by Experts

The correct Answer is:
(d)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Sow that x_1 hat i+y_1 hat j+z_1 hat k ,x_2 hat i+y_2 hat j+z_2 hat k ,a n dx_3 hat i+y_3 hat j+z_3 hat k , are non-coplanar if |x_1|>|y_1|+|z_1|,|y_2|>|x_2|+|z_2|a n d|z_3|>|x_3|+|y_3| .

If the vectors xhati+hatj+hatk,hati+yhatj+hatk and hati+hatj+zhatk are coplanar where, x ne1,y ne1 and z ne1 , then prove that (1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1

If three points A, B and C have position vectors hati + x hatj + 3 hatk, 3 hati + 4 hatj + 7 hatk and y hati -2hatj - 5 hatk respectively are collinear, then (x, y) =

The component of vector A=a_(x)hati+a_(y)hatj+a_(z)hatk and the directioin of hati-hatj is

If (x,y,z) ne (0,0,0) and (hati + hatj +3hatk )x + (3 hati - 3 hatj + hatk )y +(-4 hati + 5 hatj ) z = a (x hati + y hatj + z hatk ), then the values of a are

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=-2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

Let veca=hati+2hatj+3hati, vecb=hati-hatj+2hatk and vecc=(x-2)hati-(x-3)hatj-hatk . If vecc lies in the plane of veca and vecb , then (1)/(x) is equal to

The vectors veca=xhati-2hatj+5hatj and vecb=hati+yhatj-zhatk are collinear if (A) x=1,y=-2,z=-5 (B) x=1/2,y=-4,z=-10 (C) x=-1/2,y=4,z=10 (D) none of these

If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= zhati + xhatj+ yhatk , " then " vecaxx (vecbxx vecc) is (a)parallel to ( y- z) hati + (z - x) hatj + (x -y) hatk (b)orthogonal to hati + hatj + hatk (c)orthogonal to ( y+z) hati + ( z + x) hatj + ( x + y) hatk (d)orthogonal to xhati + yhatj + zhatk

Let x_1y_1z_1,x_2y_2z_2 and x_3y_3z_3 be three 3-digit even numbers and Delta=|{:(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3):}| . then Delta is

ARIHANT MATHS ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equi...

    Text Solution

    |

  2. A, B, C and D are four points in space. Using vector methods, prove th...

    Text Solution

    |

  3. Show that x(1) hati+y(1) hatj+ z1hatk, x2hati+y2hatj+z2hatk and x3hati...

    Text Solution

    |

  4. The position vectors of points of intersection of three planes rcdotn1...

    Text Solution

    |

  5. A pentagon is formed by cutting a triangular corner from a rectangular...

    Text Solution

    |

  6. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  7. A plane 2x+3y+5z=1 has a point P which is at minimum distance from lin...

    Text Solution

    |

  8. The locus of point which moves in such a way that its distance from th...

    Text Solution

    |

  9. A cube C={(x, y, z)|o le x, y, zle1} is cut by a sharp knife along the...

    Text Solution

    |

  10. A ray of light is sent through the point P(1,2,3) and is reflected on ...

    Text Solution

    |

  11. Find dy/dx if 2x-3sinx=2y

    Text Solution

    |

  12. The shortest distance between any two opposite edges of the tetrahedro...

    Text Solution

    |

  13. The angle between the pair of planes represented by equation 2x^(2)-2y...

    Text Solution

    |

  14. Let (p, q, r) be a point on the plane 2x+2y+z=6, then the least value ...

    Text Solution

    |

  15. The four lines drawing from the vertices of any tetrahedron to the cen...

    Text Solution

    |

  16. The shorteast distance from (1, 1, 1) to the line of intersection of t...

    Text Solution

    |

  17. The shortest distance between the two lines L1:x=k1, y=k2 and L2: x=k3...

    Text Solution

    |

  18. A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(l(3),m(3),n(3)):}] and B=[{:(p...

    Text Solution

    |

  19. ABCD is a tetrahedron such that each of the triangleABC, triangleABD a...

    Text Solution

    |

  20. In a regular tetrahedron, if the distance between the mid points of op...

    Text Solution

    |