Let a, b, c be three distinct real numbers, none equal to one. If the vectors a i+j+k, i+b j+k and i+j+c k are coplanar, then 1/(1-a)+1/(1-b)+1/(1-c) is equal to:

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q5748

JEE Main 202312 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

a, b, c

be three distinct real numbers, none equal to one. If the vectors

a \hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+b \hat{j}+\hat{\mathrm{k}}

and

\hat{\mathrm{i}}+\hat{\mathrm{j}}+c \hat{\mathrm{k}}

are coplanar, then

\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}

is equal to :

JEE Main 2023 · 12 Apr, Morning shift · Q5748

JEE Main 202312 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

a, b, c

be three distinct real numbers, none equal to one. If the vectors

a \hat{i}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+b \hat{j}+\hat{\mathrm{k}}

and

\hat{\mathrm{i}}+\hat{\mathrm{j}}+c \hat{\mathrm{k}}

are coplanar, then

\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}

is equal to :