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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)
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ARIHANT MATHS-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...

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

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

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

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

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  6. In a dimensional coodinate a system P, Q and R are image of a point A(...

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

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

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

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

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  11. A plane cutting the axes in P, Q, R passes through (alpha-beta, beta-g...

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

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

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

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

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

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

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

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  19. If ABCD is a tetrahedron such that each triangleABC, triangleABD and t...

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

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