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Show that the points whose position vect...

Show that the points whose position vectors are `5hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and -4 hat(i) + 3 hat(j) - hat(k)` are collinear.

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Prove that the four points with position vectors hat(i) + hat(j) + 3hat(k) , hat(i) - 2hat(j) + 2hat(k) and 2hat(i) + 2hat(k) are coplanar.

Show that the following vectors are coplanar. hat(i) - 2hat(j) + 2hat(k), 3hat(i) + 4hat(j) + 5hat(k), -2hat(i) + 4hat(j) - 4hat(k)

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

Show that the following vectors are coplanar. hat(i) + 2hat(j) + 3hat(k), -2hat(i) - 4hat(j) + 5hat(k), 3hat(i) + 6hat(j) + hat(k)

Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION B (60 MARKS)
  1. Evaluate int e^(x) ((1- sin x)/( 1- cos x) ) dx

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  2. Find the area of the region bounded by the curve y=x^(3) and the lines...

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  3. Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 ...

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  4. Find the vector equation of the plane passing through the points 3 hat...

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  5. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  6. Find the equation in vector and Cartesian from of the plane passing th...

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  7. Prove that sin( cos^(-1) ""(3)/(5) + sin^(-1)""(5)/(13) ) = (63)/(65)

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  8. Answer any three questions (b) A house wife wishes to mix together t...

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  9. Answer any three questions (c) Show that f: [-1,1] to R, given by f(...

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  10. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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  11. Answer any three questions (e) If a gt b gt c gt0, then prove that c...

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  12. A bag contains 6 black and 3 white balls. Another bag contains 5 black...

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  13. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  14. Answer any three questions (c) If [{:(2,-1),(1,0),(-3,4):}]A = [{:(-...

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  15. If A = [{:(2,5),(2,1):}] and B = [{:(4,-3),(2,5):}], verify that |AB| ...

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  16. The odds against A solving a certain problem are 4 to 3 and the odds i...

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  17. Find the equations of all the lines of slope 2 and that are tangent to...

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  18. Prove that the function f(x) = tan x -4x is strictly decreasing on (- ...

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  19. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

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  20. If (cosx)^(y)=(cosy)^(x), then find (dy)/(dx).

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