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Two adjacent sides of a parallelogram AB...

Two adjacent sides of a parallelogram ABCD are `2hati+4hatj -5 hatkand hati+2hatj+3hatk`. Then the value of `|vec(AC)xxvec(BD)|` is

A

`20sqrt5`

B

`22sqrt5`

C

`24sqrt5`

D

`26sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
b
`|vec(AC) xx vec(BD)|=2 |vec(AB)xxvec(AD)|`
`2|{:(hati,hatj,hatk),(2,4,-5),(1,2,3):}|`
`|2[hati(12+10)-hatj (6+5)+hatk (4-4)]|`
`|2[22hati -11 hatj]|`
`22 |[2hati - hatj]|`
`22xx sqrt5`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca, vecb,vecc are unit vectors such that veca.vecb = 0= veca.vecc...

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  2. about to only mathematics

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  3. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

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  4. If hata,hatb and hatc are three unit vectors inclined to each other at...

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  5. Let the pair of vector veca,vecb and vecc,vecd each determine a plane....

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  6. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

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  7. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

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  8. Vectors 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

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  9. The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k ...

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  10. The value of x for which the angle between veca=2x^(2)hati+4xhatj + ha...

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  11. If vectors veca and vecb are two adjacent sides of parallelograsm then...

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  12. A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ...

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  13. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

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  14. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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  15. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+la...

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  16. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

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  17. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

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  18. G is the centroid of triangle A B Ca n dA1a n dB1 are rthe midpoint...

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  19. Points vec a , vec b , vec c ,a n d vec d are coplanar and (s inalpha...

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  20. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

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