A line \( L \) passing through origin is perpendicular to the lines
\[
\begin{array}{l}
L_{1}:... VIDEO
A line \( L \) passing through origin is perpendicular to the lines
\[
\begin{array}{l}
L_{1}: \vec{r}=(3+t) \hat{i}+(-1+2 t) \hat{j}+(4+2 t) \hat{k} \\
L_{2}: \vec{r}=(3+2 s) \hat{i}+(3+2 s) \hat{j}+(2+s) \hat{k}
\end{array}
\]
If the co-ordinates of the point in the first octant on \( L_{2} \) at a distance of \( \sqrt{17} \) from the point of intersection of \( L \) and \( L_{1}^{\prime} \) are \( (a, b, c) \) then \( 18(a+b+c) \) is equal to
π²PW App Link - https://bit.ly/YTAI_PWAP
πPW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-09 The locus of a point which moves in such a way that its distance from the line \( \frac{x}{1}=\f... 2023-06-09 The shortest distance between the line \( x=y=z \) and the line \( 2 x+y+z-1=0,3 x+y+2 z-2=0 \)
... 2023-06-09 Let \( O \) be the origin and \( \overrightarrow{O A}=2 \hat{i}+2 \hat{j}+\hat{k}, \overrightarr... 2023-06-09 A plane cutting the axes in \( P, Q, R \) passes through \( (\alpha-\beta, \beta-\gamma, \gamma-... 2023-06-09 Let \( a \) and \( b \) be positive real numbers. Suppose \( \overrightarrow{P Q}=a \hat{i}+b \h... 2023-06-09 Let \( \hat{i}, \hat{j} \) and \( \hat{k} \) be the unit vectors along the three positive coordi... 2023-06-09 If a variable plane cuts the coordinate axes in \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \... 2023-06-09 \( \vec{p}, \vec{q} \), and \( \vec{r} \) are three mutually perpendicular vectors of the same m... 2023-06-09 Let \( \vec{u}, \vec{v} \) and \( \vec{w} \) be vectors in three-dimensional space, where \( \ve... 2023-06-09 Let \( A B C \) be a triangle such that \( \overrightarrow{B C}=\vec{a}, \overrightarrow{C A}=\v... 2023-06-09 A line \( L \) passing through origin is perpendicular to the lines
\[
\begin{array}{l}
L_{1}:... 2023-06-09 A line is perpendicular to \( x+2 y+2 z=0 \) and passes through \( (0,1,0) \). The perpendicular... 2023-06-09 Two lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and \( \frac{x-3}{1}=\frac{y-k}{2}=z \... 2023-06-09 Point \( (\alpha, \beta, \gamma) \) lies on the plane \( x+y+z=2 \). Let \( \vec{a}=\alpha \hat{... 2023-06-09 For \( p0 \), a vector \( \vec{v}_{2}=2 \hat{i}+(p+1) \hat{j} \) is obtained by rotating the vec... 2023-06-09 Let \( \vec{p}=2 \hat{i}+3 \hat{j}+\hat{k} \) and \( \vec{q}=\hat{i}+2 \hat{j}+\hat{k} \) be two... 2023-06-09 Let a vector \( \vec{a} \) be coplanar with vectors \( \vec{b}=2 \hat{i}+\hat{j}+\hat{k} \) and ... 2023-06-09 If the projection of the vector \( \hat{i}+2 \hat{j}+\hat{k} \) on the sum of the two vectors \(... 2023-06-09 Let \( \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k} \) and \( \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat... 2023-06-09 Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |2 \vec{a}+3 \vec{b}|=|3 \vec{a}... 2023-06-09 Let \( \vec{a}, \vec{b}, \vec{c} \) be three mutually perpendicular vectors of the same magnitud...