JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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The co-ordinates of the point

P

on the line

\mathbf{r}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})+\lambda(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})

which is nearest to the origin is

View answer and explanation

Correct option: A

\left(\frac{2}{3}, \frac{4}{3}, \frac{2}{3}\right)

Option A (

\left( \frac{{2}}{{3}}, \frac{{4}}{{3}}, \frac{{2}}{{3}} \right)

) is correct because it is the point on the line closest to the origin, found by minimizing the distance from the origin to a general point on the line.

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 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 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