Show that the lines {r}={a}+λ {b} and ...

CBSE Class 12 Math 2020 Outside Delhi Set 1 Solved Paper

Question : 36 of 36

Marks: +1, -0

Show that the lines

\vec{r}=\vec{a}+\lambda \vec{b}

and

\vec{r}=\vec{b}+\mu \vec{a}

are coplanar and the plane containing them is given by

\vec{r}\cdot(\vec{a}\times \vec{b})=0

Solution: 👈: Video Solution

Condition for Coplanarity of Two Lines in Vector Form

If the lines

\vec{r}=\vec{a}_1+\lambda \vec{b}_1

and

\vec{r}=\vec{a}_2+\mu \vec{b}_2

are coplanar,

then

\vec{r}\cdot (\vec{b}_1\times \vec{b}_2) =\vec{a}_2\cdot (\vec{b}_1\times \vec{b}_2)

Substituting above values in this equations

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