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The coordinates of the point `P` on the line ` vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k)` which is nearest to the origin is a. `(2/4,4/3,2/3)` b. `(-2/3,-4/3,2/3)` c. `(2/3,-4/3,2/3)` d. none of these

A

`((2)/(3), (4)/(3), (2)/(3))`

B

`(-(2)/(3), -(4)/(3), (2)/(3))`

C

`((2)/(3), (4)/(3), -(2)/(3))`

D

None of these

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The correct Answer is:
(a)
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ARIHANT MATHS ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The radius of the circle in which the sphere x^(2)=y^(2)+z^(2)+2z-2y-4...

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  2. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  3. The coordinates of the point P on the line vec r=( hat i+ hat j+ h...

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  4. Find 3-dimensional vectors vec v1,vec v2,vec v3 satisfying vec v1* ve...

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  5. The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equi...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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