Mathematics

The distance of point $$\left(1,0,2\right)$$ from the point of intersection of the line $$\dfrac{x-2}{3}=\dfrac{y+1}{4}=\dfrac{z-2}{12}$$ and the plane $$x-y+z=16$$ is


ANSWER

$$13$$


SOLUTION

$$\displaystyle \frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}=\lambda $$

$$x=3\lambda +2$$  $$y=4\lambda -1$$  $$z=12\lambda +2$$

$$(x,y,z)\rightarrow x-y+z=16$$ should satisfy

$$3\lambda +2-(4\lambda -1)+12\lambda +2=16$$

$$3\lambda +2-4\lambda +1+12\lambda +2=16$$

$$11\lambda =11$$

$$\lambda =1$$

$$(x,y,z)=(5,3,14)$$ - point of intersection of line

Distance b/w (1,0,2) & (5,3,14)

$$d=\sqrt{(5-1)^{2}+(3-0)^{2}+(14-2)^{2}}$$

$$=\sqrt{16+9+144}$$

$$=\sqrt{169}$$

$$d=13$$

$$\therefore $$ option C = 13
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Single Correct Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
If the sum of two adjacent angles is $$100^{\circ}$$ and one of them is $$35^{\circ}$$, then the other is :
  • A. $$70^{\circ}$$
  • B. $$135^{\circ}$$
  • C. $$145^{\circ}$$
  • D. $$65^{\circ}$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Single Correct Medium
______ angles have common side and vertex but they don't overlap.
  • A. Vertical
  • B. Corresponding
  • C. Alternate
  • D. Adjacent

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Single Correct Medium
If l$$\displaystyle \parallel $$m and m $$\displaystyle \parallel $$ n then
  • A. l$$\displaystyle \parallel $$p
  • B. l$$\displaystyle \parallel $$q
  • C. m$$\displaystyle \parallel $$q
  • D. l$$\displaystyle \parallel $$n

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 One Word Medium
Find complementary angle of $$23^{\circ}$$.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Subjective Medium
From the adjoining figure find $$x$$,  i $$AOB$$ is a straight line. Hence complete the following 
Which is an acute angle?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer