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Assertion (A): The area of the triangle ...

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 ?

A

Both (A) and (R ) are true and (R ) is the correct explanation of (A)

B

Both (A) and (R ) are true and (R ) is not the correct explanation of (A)

C

(A) is true, (R ) is false

D

(A) is false, (R ) is true

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The correct Answer is:
A
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AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Practice Exercise
  1. The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and ve...

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  2. If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0...

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  3. Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, ...

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  4. The area of the parallelogram is 4sqrt29 sq.u. If one of adjacent side...

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  5. ABCD is a quadrilateral with vec(AB)= vec(a), vec(AD)= vec(b) and vec(...

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  6. The perpendicular distance from A(1, 4, -2) to BC, where B= (2, 1, -2)...

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  7. If vec(AB)= vec(b) and vec(AC)= vec( c), then the length of the perpen...

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  8. The torque about the point 2i + j - K of a force represented by 4i + k...

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  9. Assertion (A): The torque about the point 3vec(i)-vec(j) + 3vec(k) of ...

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  10. If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx v...

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  11. (2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec...

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  12. If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k),...

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  13. If |bar(P)| = 2, |bar(q)| = 3 and (bar(p),bar(q)) = (pi)/6, then find ...

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  14. If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(...

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  15. The vector area of the rectangle whose adjacent sides are p vec(i), q ...

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  16. If vec(r )= x vec(i) + y vec(j) + z vec(k) then (vec(r ) xx vec(i)).(v...

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  17. If u and v are unit vectors and theta is the acute angle between them,...

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  18. A unit vector normal to the plane through the points vec(i), 2vec(j) ...

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  19. If the vectors vec(a), vec(b), vec(c ) are represents the sides vec(BC...

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  20. For any vector vec(a), the value of (vec(a) xx vec(i))^(2) + (vec(a) x...

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