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Find the area of a triangle having the p...

Find the area of a triangle having the points`A(1, 1, 1)`, `B(1, 2, 3)`and `C(2, 3, 1)`as its vertices.

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To find the area of the triangle formed by the points \( A(1, 1, 1) \), \( B(1, 2, 3) \), and \( C(2, 3, 1) \), we can follow these steps: ### Step 1: Find the vectors \( \vec{AB} \) and \( \vec{AC} \) The vector \( \vec{AB} \) is calculated as follows: \[ \vec{AB} = B - A = (1, 2, 3) - (1, 1, 1) = (1-1, 2-1, 3-1) = (0, 1, 2) \] ...
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NCERT-VECTOR ALGEBRA-SOLVED EXAMPLES
  1. Let vec a= hat i+2 hat jand vecb=2 hat i+ hat j. Is | vec a|=| vec b...

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  2. Find unit vector in the direction of vector vec a=2 hat i+3 hat j+ ha...

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  3. Find a vector in the direction of vector vec a= hat i-2 hat jthat has...

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  4. If with reference to the right handed system of mutually perpendicula...

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  5. Find | vec a xx vec b|,if vec a=2 hat i+ hat j+3 hat k and vec b=3 h...

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  6. Find a unit vector perpendicular to each of the vectors ( veca+ vecb)...

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  7. For any two vectors vec a and vec b, we always have |vec a+ vec b|<=|v...

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  8. Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 h...

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  9. Write all the unit vectors in X Y-p l a n edot

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  10. If hat i+ hat j+ hat k ,2 hat i+5 hat j ,3 hat i+2 hat j-3 hat kand ...

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  11. Find the area of a triangle having the pointsA(1, 1, 1), B(1, 2, 3)and...

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  12. Find the area of a parallelogram whose adjacent sides are given by th...

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  13. Let vec a , vec b and vec cbe three vectors such that | vec a|=3,|...

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  14. Three vectors vec( a), vec(b) and vec(c) satisfy the co...

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  15. Find lambda if the vectors veca= hat i+3\ hat j+ hat k , vecb=2 hat...

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  16. Prove that [ -> a , -> b , -> c+ -> d]=[ -> a , -> b , -> c]+[ -> a , ...

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  17. Show that the vectors -> a= hat i-2\ hat j+3 hat k , -> b=\ 2 hat i...

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  18. Find vec a . ( vec b xx vec c), if vec a=2 hat i+ hat j+3 hat k , ve...

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  19. Prove that [ veca+ vecb , vecb+ vecc , vecc+ veca]=2[ veca , vecb , ve...

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  20. Show that the four points A, B, C and D with position vectors4 hat i+...

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