JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

1 Easy

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Analyzing +4 | -1

If the vertices of a triangle at

O\left( {0,0} \right),A\left( {a,0} \right)

and

B\left( {0,a} \right).

Then, the distance between its circumcentre and orthocentre is

View answer and explanation

Correct option: B

\frac{a}{{\sqrt 2 }}

Option B (

\frac{a}{{\sqrt 2 }}

) is correct because the orthocenter is at the origin and the circumcenter is the midpoint of the hypotenuse, allowing us to calculate the distance between them.

More Questions from 3D GEOMETRY SYSTEM

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The mid point of the line joining the points

\left( { - 10,\;8} \right)

and

\left( { - 6,\;12} \right)

divides the line joining the points

\left( {4,\; - 2} \right)

and

\left( { - 2,\;4} \right)

in the ratio The equation of the plane perpendicular to the

y z

-plane and passing through the points

(1,-2,4)

and

(3,-4

5)

is The value of

p

for which the lines

2 x+y-3=0

3 x-y-2=0

and

x-p y+5=0

may intersect at a point is The coordinates of the foot of the perpendicular drawn from the point

A(1,0,3)

to the join of the points

B(4,7,1)

and

C(3,5,3)

are The area of the triangle formed by the three lines

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

and

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

is
If

\mathrm{A}(1,-1,2), \mathrm{B}(5,7,-6), \mathrm{C}(3,4,-10)

and

\mathrm{D}(-1,-4,-2)

are the vertices of a quadrilateral

\mathrm{ABCD},

then its area is: