Let a=i+2 j+3 k, b=i-j+2 k and c=5 i-3 j+3 k be three vectors. If r is a vector such that, r × b=c × b and r · a=0, then 25|r|² is equal to:

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 31 Jan, Evening shift · Q5831

JEE Main 202331 Jan, Evening shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}

and

\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}

be three vectors. If

\vec{r}

is a vector such that,

\vec{r} \times \vec{b}=\vec{c} \times \vec{b}

and

\vec{r} \cdot \vec{a}=0

, then

25|\vec{r}|^{2}

is equal to :

JEE Main 2023 · 31 Jan, Evening shift · Q5831

JEE Main 202331 Jan, Evening shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}

and

\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}

be three vectors. If

\vec{r}

is a vector such that,

\vec{r} \times \vec{b}=\vec{c} \times \vec{b}

and

\vec{r} \cdot \vec{a}=0

, then

25|\vec{r}|^{2}

is equal to :