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For a sphere, ends of a diameter have po...

For a sphere, ends of a diameter have position vectors `bara and -bara`, when vector equation of sphere is
Statement-I : `|barr|=|bara|`
Statement-II : `(barr+bara)*(barr-bara)=0`
Statement-III : `barr.bara=0`
Which of the above statements are true

A

only I, II

B

only II, III

C

only I, III

D

I, II, III

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The correct Answer is:
A
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DOT PRODUCT OF TWO VECTORS
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  2. Equation of sphere whose centre is at 7bari-4barj+bark and radius |3b...

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  3. The cartesian equation of the sphere whose centre is C(5, 2, 3) and w...

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  4. The centre and radius of the sphere r^(2) - 2r. (3i + 4j - 5k) + 1 = 0...

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  5. Equation of the sphere described on the join of the points bara=2bari+...

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  6. The radius of the sphere (barr-2bari+3barj-bark). (barr+3bari-barj+2b...

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  7. The cartesian equation of the sphere whose diameter end points are A(1...

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  8. Arrangement of raddi of the following spheres in de-scendin order is ...

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  9. The cartesian equation of the sphere with centre (2, -1, 3) and radi...

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  10. Radius of the sphere r^(2) -2r.(3i+4j-5k)+1=0 is

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  11. Positiion vector of centre of the sphere barr^(2)-barr.(bari+barj+bar...

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  12. The centre and radius of the sphere (bar r-3bari-4barj+5bark)*(barr-2...

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  13. If 2bari and 4bark are the position vectors of the extremities of a di...

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  14. If the position vector of one end A of a diameter AB of the sphere |ba...

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  15. For a sphere, ends of a diameter have position vectors bara and -bara,...

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  16. If |barc|^(2)=60 and barc xx (bari+2barj+5bark)=bar0 then a value of b...

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  17. If barx, bary, barz are three unnit vectors in three - dimensional spa...

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  18. |bara|=2, |barb|=3 and |2bara-barb|=5 then |2bara+barb| equals:

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  19. A vector barn is inclined to x-axis at 45^(0), to y-axis at 60^(0) and...

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  20. If bara, barb, barc are unit vectors satisfying bara-sqrt(3)barb+barc=...

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