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

$13$

##### 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

You're just one step away

Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### 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

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

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

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

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

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

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