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MCQMediumJEE Main 2023 · 29 January, Shift 2Cross Product

Mathematics Question from JEE Main 2023 · 29 January, Shift 2

Let a⃗=4i^+3j^\vec{a} = 4\hat{i} + 3\hat{j}, b=3i^−4j^+5k^b = 3\hat{i} - 4\hat{j} + 5\hat{k}, and cc be a vector such that (a⃗×b⃗)⋅c⃗+25=0(\vec{a} \times \vec{b}) \cdot \vec{c} + 25 = 0, c⃗⋅(i^+j^+k^)=4\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = 4, and the projection of c⃗\vec{c} on a⃗\vec{a} is 11. Then the projection of c⃗\vec{c} on b⃗\vec{b} equals:

  • A

    52\frac{5}{\sqrt{2}}

  • B

    12\frac{1}{\sqrt{2}}

  • C

    15\frac{1}{\sqrt{5}}

  • D

    52\frac{\sqrt{5}}{\sqrt{2}}

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