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Two adjacent sides of a parallelogram ...

Two adjacent sides of a parallelogram `A B C D` are `2 hat i+4 hat j-5 hat k` and ` hat i+2 hat j+3 hat k` . Then the value of `|A CxxB D|` is a. `20sqrt(5)` b. `22sqrt(5)` c. `24sqrt(5)` d. `26sqrt(5)`

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 PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  2. about to only mathematics

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  3. Two adjacent sides of a parallelogram A B C D are 2 hat i+4 hat j-5 ...

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  4. If hat a , hat b ,a n d hat c are three unit vectors inclined to ea...

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  5. Let the pairs a , b,and c ,d each determine a plane. Then the planes a...

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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 3 vec a-5 vec b and 2 vec a+ vec b are mutually perpendicular....

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  9. The unit vector orthogonal to vector -hat i+ hat j+2 hat k and maki...

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  10. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

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  11. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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  12. A parallelogram is constructed on 2 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. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

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

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  16. A vector of magnitude sqrt(2) coplanar with the vector vec a= hat i+ ...

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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 ABC and A1 and B1 are the midpoints of...

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  19. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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  20. If vec aa n d vec b are any two vectors of magnitudes 1 and 2, resp...

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