An equation of a plane containing the lines $r = a_{1} + t b_{1}$ and $r = a_{2} + t b_{2}$ where $[a_{2} - a_{1}, b_{1}, b_{2}] = 0$ is

[r - a_{1}, b_{1}, b_{2}] = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

[r - a_{2}, b_{1}, b_{2}] = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[r - a_{2}, a_{1}, b_{2}] = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[r - a, a_{2}, b_{2}] = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $[r - a_{1}, b_{1}, b_{2}] = 0$
Given lines
$\to r = a_{1} + t b_{1}$
$\to r = a_{2} + t b_{2}$
$[a_{2} - a_{1}, b_{1}, b_{2}] = 0$ i.e. $a_{2} - a_{1}, b_{1}, b_{2}$ are coplanar
normal vector of plane $b_{1} \times b_{2}$
the plane contains $a_{1} a n d a_{2}$ but the position vector of plane is $a_{1}$ because $[a_{2} - a_{1}, b_{1}, b_{2}] = 0$
eq of plane
$(\to r - a) \cdot^(n) = 0$
$(\to r - a_{1}) \cdot (b_{1} \times b_{2}) = 0$
$[\to r - a_{1}, b_{1}, b_{2}] = 0$

Suggest Corrections

Similar questions

Unique point is obtained for the pair of equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 if

The condition for a pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to be parallel is

Q. If the lines

\vec{r} = \vec{a_{1}} + λ \vec{b_{1}} a n d \vec{r} = 2 \vec{a_{2}} + λ \vec{b_{2}}

are coplanar, then

\frac{[\vec{a_{1}} \vec{b_{1}} \vec{b_{2}}]}{[\vec{a_{2}} \vec{b_{1}} \vec{b_{2}}]}

= _____________.

What can you tell about the ratio of coefficients of the lines $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 from the graph ?

Parallel lines are obtained for the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ if

Join BYJU'S Learning Program

An equation of a plane containing the lines r=a1+tb1and r=a2+tb2 where [a2−a1,b1,b2]=0 is

An equation of a plane containing the lines $r = a_{1} + t b_{1}$ and $r = a_{2} + t b_{2}$ where $[a_{2} - a_{1}, b_{1}, b_{2}] = 0$ is