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If the vertices of an equilateral triang...

If the vertices of an equilateral triangle are `A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3)` then show that `|(x_1, y_1,2),(x_2, y_2, 2),(x_3,y_3,2)|^2` `= 3a^4`, 'a' being the length of each side of the triangle.

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. For what value of k the points (k,2-2k),(-k+1,2k)and (-4-k,6-2k) are c...

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  2. Show that the points (a+5, a-4), (a-2, a +3) and (a,a) do not lie on a...

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  3. If the vertices of an equilateral triangle are A(x1,y1), B(x2,y2) and ...

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  4. Find the adjoint of each of the following matrices: [(1,0),(0,1)]

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  5. Find the adjoint of the following matrices: {:[(a,b),(c,d)]

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  6. Find the adjoint of each of the following matrices: [(cos theta, sin t...

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  7. Find the adjoint of each of the following matrices: [(1, tan(theta//2)...

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  8. Find the adjoint of the following matrices: [(3,4),(5,7)]

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  9. Find the adjoint of each of the following matrices: [(2,3),(5,1)] veri...

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  10. Find the adjoint of the following matrices: [(1,2,3),(2,3,2),(3,3,4)]

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  11. Find the adjoint of the following matrices: [(1,-1,2),(3,1,-2),(1,0,3)...

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  12. Find the adjoint of the following matrices: [(6,-7,8),(1,-3,1),(2,1,-4...

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  13. Find the adjoint of the following matrices: [(1,-1,2),(3,0,-2),(1,0,3)...

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  14. Find the adjoint of the following matrices: A = [(1,-1,1),(2,3,0),(18,...

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  15. For the matrix A = [(cos alpha, -sinalpha, 0),(sinalpha, cosalpha, 0),...

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  16. Find the inverse of each of the folowing matrices: [(3,1),(-1,2)]

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  17. Find the inverse of each of the folowing matrices: [(2,5),(1,3)]

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  18. Find the inverse of each of the folowing matrices: [(2,3),(5,7)]

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  19. Find the inverse of each of the folowing matrices: [(1,0),(0,1)]

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  20. Find the inverse of each of the folowing matrices: [(2,5),(-3,1)]

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