JEE MATHEMATICS MCQ: 3D PLANES

1 Hard

1 of 1

Application +4 | -1

(x,\,y,\,z)

be an arbitrary point lying on a plane

P

, which passes through the points

\mathrm{(42,}\,\mathrm{0,}\,\mathrm{0),}\,\,\mathrm{(0,}\,\mathrm{42,}\,\mathrm{0)}

and

\mathrm{(0,}\,\mathrm{0,}\,\mathrm{42)}

, then the value of expression

3 + \frac{{x - 11}}{{{{\left( {y - 19} \right)}^2}{{\left( {z - 12} \right)}^2}}} + \frac{{y\, - \,19}}{{{{\left( {x - 11} \right)}^2}{{\left( {z - 12} \right)}^2}}}\, + \frac{{z - 12}}{{{{\left( {x - 11} \right)}^2}{{\left( {y - 19} \right)}^2}}} - \frac{{x\mathrm{ } + \mathrm{ }y\mathrm{ } + z}}{{14\left( {x - 11} \right)\left( {y - 19} \right)\left( {z - 12} \right)}}

is equal to

View answer and explanation

Correct option: B

Option B (3) is correct because by substituting the plane equation into the expression and simplifying using the given condition, the expression reduces to 3.

More Questions from 3D PLANES

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Let

\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}

lie on the plane

p x-q y+

z=5

, for some

p, q \in \mathbb{R}

. The shortest distance of the plane from the origin is : If the planes

x-c y-b z=0, c x-y+a z=0

and

b x+a y-z=0

pass through a straight line, then the value of

a^2+b^2+c^2+2 a b c

is: Let the plane

2 x-3 y+9 z=0

P

, the equation of line passing through

(0,1,-1)

and lying-in plane

4 x-2 y+7 z+9=0

& parallel to

P

is: A plane which passes through the point

(3,2,0)

and the line

\frac{x-4}{1}=\frac{y-7}{5}=\frac{z-4}{4}

is The plane

a x+

=0

is rotated through an angle

\alpha

about its line of intersection with the plane

z=0

. If the equation of plane in new position is

\mathrm{ax}+\mathrm{by} \pm \mathrm{z} \sqrt{\mathrm{a}^2+\mathrm{b}^2} \tan \alpha+\mathrm{c}=0

. Find c. A variable plane passes through a fixed point

(3,2,1)

and meets

x, y

and

z

axes at

A, B

and

C

respectively. A plane is drawn parallel to

y z

-plane through

A

, a second plane is drawn parallel

z x

-plane through

B

and a third plane is drawn parallel to

x y

-plane through

C

. Then the locus of the point of intersection of these three planes, is