Let the vectors u₁=i+j+a k, u₂=i+b j+k and u₃=c i+j+k be coplanar. If the vectors v₁=(a+b) i+c j+c k, v₂=a i+(b+c) j+a k and v₃=b i+b j+(c+a) k are also coplanar, then 6(a+b+c) is equal to:

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q5751

JEE Main 20238 Apr, Evening shiftMathematicsMediumVector Algebra184× since 2002

Let the vectors

\vec{u}_{1}=\hat{i}+\hat{j}+a \hat{k}, \vec{u}_{2}=\hat{i}+b \hat{j}+\hat{k}

and

\vec{u}_{3}=c \hat{i}+\hat{j}+\hat{k}

be coplanar. If the vectors

\vec{v}_{1}=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \vec{v}_{2}=a \hat{i}+(b+c) \hat{j}+a \hat{k}

and

\vec{v}_{3}=b \hat{i}+b \hat{j}+(c+a) \hat{k}

are also coplanar, then

6(\mathrm{a}+\mathrm{b}+\mathrm{c})

is equal to :