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Find the equation of the plane which pas...

Find the equation of the plane which passing through the point `hati + hatj + hatk` and parallel to the plane `vec r.(2hati - hatj + 2hatk)` = 0.

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Find the equation of the plane which passing through the points hati+ hatj+ hatk and parallel to the plane vecr.(2 hati-hatj+2 hatk)=5

Find the vector equation of a plane through the point hati+ hat j+hat k and parallel to the plane vecr.(2 hat i-hatj +2 hatk)=5 .

Find the vector equation of the line passing through the point (2,-3,1) and parallel to the planes vec r.(2hati-3hatj-hatk)=3 and vec r.(hati+hatj-hatk)=4 .

Find the vector equations of the plane passing through the points 3 hati+ 4 hatj+2 hatk, 2hati-2 hatj -hatk and 7 hati+6 hatk .

The vector equation of the line passing through the point (3, -1, 2) and parallel to the vector 2hati-3hatj+4hatk is -

Find the equation of the plane passing through the line of intersection of the planes vec r.(hati+hatj+hatk)=1 and vec r.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

Find the equation of the plane passing through the line of intersection of the plane vecr.(hati+3 hatj)+6=0 and vecr.(3 hati- hatj-4k)=0 which is at a unit distance from the origin.

Find the vector equation of a line which passes throught the point with position vector hati - 2hat j+4hatk and is in the direction of hati + 2hatj - hatk . Also reduce it to cartesian form.

Find the equation of a line passing through the point P(2,-1,3) and perpendicular to the lines vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vec r=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hati+hatj+5hatk)+lambda(3hati-hatj-5hatk) Also show that the plane contains the line vec r=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .

UNITED BOOK HOUSE-SET 14-EXERCISE
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  2. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

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  3. Find the equation of the plane which passing through the point hati + ...

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  4. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

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  5. A discrete random variable X has the following distribution: find a.

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  6. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

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  7. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  8. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

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  9. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  12. Solve:(x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

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  14. Find the vector alpha which is perpendicular to both 4 hati + 5hatj -...

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  15. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

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  16. Evaluate:underset(n rarr infty)lim 1/n[sin (pi/(2n)) +sin((2pi)/(2n))+...

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