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MCQMediumJEE Main 2023 · 1 February, Shift 2Cross Product

Mathematics Question from JEE Main 2023 · 1 February, Shift 2

Let a⃗=2i^−7j^+5k^\vec{a} = 2\hat{i} - 7\hat{j} + 5\hat{k}, b⃗=i^+k^\vec{b} = \hat{i} + \hat{k}, and c⃗=i^+2j^−3k^\vec{c} = \hat{i} + 2\hat{j} - 3\hat{k} be three given vectors. If r⃗\vec{r} is a vector such that r⃗×a⃗=c⃗×a⃗\vec{r} \times \vec{a} = \vec{c} \times \vec{a} and r⃗⋅b⃗=0\vec{r} \cdot \vec{b} = 0, then ∣r⃗∣|\vec{r}| is equal to:

  • A

    1172\frac{11}{7} \sqrt{2}

  • B

    117\frac{11}{7}

  • C

    1152\frac{11}{5} \sqrt{2}

  • D

    9147\frac{\sqrt{914}}{7}

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