the image of the point (-1,3,4) in the p...

the image of the point `(-1,3,4)` in the plane `x-2y=0` a.`(-(17)/(3),(19)/(3),4)` b.(15,11,4) c.`(-(17)/(3),(19)/(3),1)` d.`((9)/(5),-(13)/(5),4)`

`(-17/3,-19/3,4)`

(15,11,4)

`(-17/3,-19/3,1)`

`(9/5,(-13)/(5),4)`

Text Solution

Verified by Experts

The correct Answer is:

Equation of line PQ is `(x+1)/(1)=(y-3)/(-2)=(z-4)/(0)=lambda`

For some suitable value of `lambda,` coordinates of point `Q(lambda -1, 3 - 2lambda, 4) ` R is the midpoint of P and Q `therefore R=((lambda-2)/(2),(6-2lambda)/(2),4), therefore R-=(lambda/2-1,3 lambda,4)`
It satisfies `x-2y=0 rArr lambda=14/5`
`Q=(9/5,-13/5,4)`

Topper's Solved these Questions

JEE MAIN REVISION TEST -14
VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
JEE MAIN REVISION TEST 11 (2020)
VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION - 2)|4 Videos

Similar Questions

Explore conceptually related problems

Find the image of the point (0,2,3) in the line (x+3)/(5)= (y-1)/(2) = (z+4)/(3) .

Find the image of the point (2,-3,4) with respect to the plane 4x+2y-4z+3=0

The image of the point (1, 3, 4) in the plane 2x-y+z+3=0 is (3,\ 5,\ 2) b. (-3,5,\ 2) c. (3,\ 5,\ -2) d. (3,\ -5,\ 2)

The reflection of the point (2,-1,3) in the plane 3x-2y-z=9 is (A) (28/7,15/7,17/7) (B) (26/7,-15/7,17/7) (C) (15/7,26/,-17/7) (D) (26/7,17/7,-15/70)

The projections of a line segment on X, Y and Z axes are 12,4 and 3 respectively. The length and direction cosines of the line segment are a. 13; (12)/(13),4/(13),3/(13) b. 19 ;(12)/(19),4/(19),9/(19) c. 11;(12)/(11),(14)/(11),3/(12) d. none of these

The point of intersection of tangent to the curve y=x^4 at (1,1) with the normal to the same curve at (-1,1) is (A) ((17)/(15),(13)/(15)) (B) (7/5,3/5) (C) ((17)/(15),(23)/(15)) (D) does not exist

{(1/3)^(-3)-(1/2)^(-3)}-:(1/4)^(-3) = (a) (19)/(64) (b) (64)/(19) (c) (27)/(16) (d) (-19)/(64)

Which one of the following is true? (a) 1/2 (b) 3/4 (d) 1/2<9/(13)<(12)/(17)<3/4

The line (x-3)/1=(y-4)/2=(z-5)/2 cuts the plane x+y+z=17 at

Which of the following is a proper fraction? (a) (13)/(17) (b) (17)/(13) (c) (12)/5 (d) 1 3/4

VMC MODULES ENGLISH-JEE MAIN REVISION TEST -17 (2020)-MATHEMATICS

For A=133^(@), 2cos\ A/2is equal to
Text Solution
|
Let S be the set of all real numbers and Let R be a relations on s...
Text Solution
|
Negation of the conditional, ..If it rains, I shall go to school.. is:
Text Solution
|
The value of lambda, for which the line 2x - (8)/(3) lambda y =- 3 is ...
Text Solution
|
If |(1+sin^2 theta,sin^2 theta,sin^2 theta),(cos^2 theta,1+cos^2 theta...
Text Solution
|
The product of n consecutive natural numbers is always divisible by
Text Solution
|
In a triangle ABC, if sin A sin B= (ab)/(c^(2)), then the triangle is ...
Text Solution
|
The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...
Text Solution
|
Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...
Text Solution
|
Solve: {(xy)cos(xy)+sin(xy)}dx+x^2cos(xy)dy=0
Text Solution
|
If veca,vecb and vecc are non coplanar and unit vectors such that veca...
Text Solution
|
the image of the point (-1,3,4) in the plane x-2y=0 a.(-(17)/(3),(19)/...
Text Solution
|
If the letters of the word SACHIN are arranged in all possible ways...
Text Solution
|
If H(1) and H(2) are two harmonic means between two positive numbers a...
Text Solution
|
A point P moves in such a way that the ratio of its distance from two ...
Text Solution
|
If the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/...
Text Solution
|
The probability of a bomb hitting a bridge is 1/2 and two direct hits ...
Text Solution
|
Find the minimum value of |x|+|x+1/2|+|x-3|+|x-5/2|dot
Text Solution
|
If the slope of one of the lines represented by ax^(2)+2hxy+by^(2)=0 ...
Text Solution
|
The acute angle between F(1)(x)=int(2)^(x) (2t-5)dt and F(2)(x)=int(...
Text Solution
|