The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to
- $\sqrt{\frac{2}{13}}$
- $\sqrt{\frac{13}{2}}$
- $\frac{13}{2}$
- $\frac{2}{13}$
The Correct Option is B
Solution and Explanation
$d=\frac{\left|a x_{1}+b y_{1}+c\right|}{\sqrt{a^{2}+b^{2}}}$
$\therefore$ Required distance,
$d =\frac{|1+5(-1)-9|}{\sqrt{1^{2}+5^{2}}} $
$=\frac{|1-14|}{\sqrt{1+25}}=\frac{13}{\sqrt{26}}$
$=\sqrt{\frac{13}{2}}$
Top Questions on Coplanarity of Two Lines
- A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :
- JEE Main - 2023
- Mathematics
- Coplanarity of Two Lines
- The lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-K} \) and \(\frac{x-1}{K}=\frac{y-4}{2}=\frac{z-5}{1} \) are coplanar if :
- CUET (UG) - 2023
- Mathematics
- Coplanarity of Two Lines
- Let the lines l1: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l2: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to
- JEE Main - 2023
- Mathematics
- Coplanarity of Two Lines
Let \(\vec{a}, \vec{b}, \vec{c}\)
be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and
\((\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} \times \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} \times \vec{a}) \cdot (\vec{a} \times \vec{b}) = 168\), then \(|\vec{a}| + |\vec{b}| + |\vec{c}|\)| is equal to :- JEE Main - 2022
- Mathematics
- Coplanarity of Two Lines
- The perpendicular distance between the lines $9x^2- 24xy + 16y^2 + 21x- 28y+ 10 = 0$ is
- COMEDK UGET - 2010
- Mathematics
- Coplanarity of Two Lines
Questions Asked in KEAM exam
- Suppose there are 5 alike dogs, 6 alike monkeys and 7 alike horses. The number of ways of selecting one or more animals from these is
- KEAM - 2023
- permutations and combinations
Let S={\(a,b,c\)} be the sample space with the associated probabilities satisfying \(P(a)=2P(b)\) and \(P(b)=2P(c).\)Then the value of \(P(a)\) is
- KEAM - 2023
- Probability
- If, \(x∈(0,π)\) satisfies the equation \(6^{1+sinx+sin^2x....}=36\) ,then the value of \(x\) is_____.
- KEAM - 2023
- Trigonometric Functions
Which are the non-benzenoid aromatic compounds in the following?
- KEAM - 2023
- Hydrocarbons
Car P is heading east with a speed V and car Q is heading north with a speed \(\sqrt{3}\). What is the velocity of car Q with respect to car P?
- KEAM - 2023
- Motion in a plane
Concepts Used:
Coplanarity of Two Lines
Condition for Coplanarity Using Cartesian Form
The condition for coplanarity in the Cartesian form appears from the vector form.
Let's consider two points L (a1, b1, c1) & Q (a2, b2, c2) in the Cartesian plane,
Presuppose that there are two vectors q1 and q2. Their direction ratios are subjected by {x1, y1, z1}, and {x2, y2, z2} respectively.
The vector form of equation of the line in connection to L and Q can be stated as under:
LQ = (a2 – a1)i + (b2 – b1)j + (c2 – c1)k
Q1 = x1i + y1j + z1k
Q2 = x2i + y2j + z2k
Condition for Coplanarity Using Vector Form
For the derivation of the condition for coplanarity in vector form, we shall take into consideration the equations of two straight lines to be as stated below:
r1 = l1 + λq1
r2 = l2 + λq2
The condition for coplanarity in vector form is that the line in connection to the two points should be perpendicular to the product of the two vectors, q1 and q2.
SUBSCRIBE TO OUR NEWS LETTER
