MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Fundamental Theorem in 2D

The lines who...

Question

The lines whose vector equations are $\to r = \to a + t \to b$ and $\to r = \to c + s \to d$ are coplanar if..

A

(\to b - \to c) . (\to a \times \to d) = 0

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

B

(\to a - \to b) . (\to c \times \to d) = 0

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

C

(\to a - \to c) . (\to b \times \to d) = 0

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

D

(\to b - \to d) . (\to a \times \to c) = 0

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

Open in App

Solution

The correct option is C $(\to a - \to c) . (\to b \times \to d) = 0$
Given:
$L_{1} : \to r = \to a + t \to b$
$L_{2} : \to r = \to c + s \to d$
We know that $\to a, \to c$ are the fixed points lying on the line $L_{1}, L_{2}$ respectively
And $\to b, \to d$ are the direction ratios lying of the line $L_{1}, L_{2}$ respectively which are the two vectors coplanarity condition on plane.
For coplanarity we need third vector lying on the plane which can be $\to m = \to a - \to c$
Hence for Coplanar Lines $L_{1}, L_{2}$
$\Rightarrow \to m . (\to b \times \to d) = 0$
$\Rightarrow (\to a - \to c) . (\to b \times \to d) = 0$

Suggest Corrections

thumbs-up

3

Similar questions

\to a, \to b, \to c

are three non coplanar vectors and a vector

\to r

satisfying the vector equation

\to r . \to a = \to r . \to b = \to r . \to c = 1

\to a, \to b, \to c

are non-coplanar vectors

\to r . \to a = \to r . \to b = \to r . \to c = 0

\to r

is a zero vector.

\to a, \to b, \to c

are three non coplanar vectors and a vector

\to r = \frac{(\to r . \to a) (\to b \times \to c) + (\to r . \to b) (\to c \times \to a) + (\to r . \to c) (\to a \times \to b)}{λ},

then the value of

λ

\to a, \to b, \to c

are three non coplanar, non zero vectors and

\to r

is any vector in space, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

λ [\to a \to b \to c]

. Then the value of

λ

\to a, \to b, \to c

\to p, \to q, \to r

are sets of three non-coplanar unit vectors such that

\to a \cdot \to p + \to b \cdot \to q + \to c \cdot \to r = 3,

\to p, \to q

\to r

respectively are given by the vectors

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Fundamental Theorem in 2D

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon