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The area of the triangle with vertices (...

The area of the triangle with vertices (1,2,3), (2,5,-1), (-1,1,2) is

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The correct Answer is:
`-(3)/(2) (vec(i) + vec(j) + vec(k)), (3 sqrt3)/(2)` sq. units
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Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, -1) and (-1, 1, 2) is (1)/(2) sqrt155 sq units. Reason (R ): The area of the triangle with vertices vec(a), vec(b), vec(c ) is (1)/(2) |vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)| Which of the following is correct ?

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AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Exercise-3.1 (very Short Answer Questions)
  1. If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) ...

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  2. If |bar(a)|=2, |bar(b)|=3, (bar(a), bar(b))= pi//6, then find (bar(a) ...

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  3. If |bar(a) xx bar(b)|= bar(a).bar(b), then find the angle between the ...

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  4. If theta is the angle between the vectors bar(i) + bar(j) , bar(j) + b...

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  5. If 4bar(i) + (2p)/3 bar(j)+ pbar(k) is parallel to the vector bar(i) ...

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  6. If bar(p) = xbar(i) + ybar(j) + zbar(k), find the value of |bar(p) xx ...

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  7. For any vector bar(a) show that |bar(a) xx bar(i)|^(2) + |bar(a) xx ba...

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  8. Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + b...

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  9. Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k).

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  10. If |bar(a)| = 13, |bar(b)| = 5, and bar(a).bar(b) = 60, then find |bar...

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  11. If bar(a) = bar(i) + 2bar(j) + 3bar(k), bar(b) = 3bar(i) +5bar(j) -bar...

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  12. Find the area of the triangle having (3bar(i)+4bar(j)),(-5bar(i)+7bar(...

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  13. The area of the triangle with vertices (1,2,3), (2,5,-1), (-1,1,2) is

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  14. Find the area of the parallelogram whose adjacent sides are bar(a) = 2...

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  15. Find the vector area and area of the parallelogram having bar(a) = bar...

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  16. Find the area of the parallelogram whose diagonals are 3bar(i) + bar(j...

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