Verified Solution • 2025–26 Session moderate

QNEET-2022-Ph-547: NEET 2022 Physics - Class 11 NEET-2022-Ph-547 Solution: If \( {F} = 2 {i} + {j} - {k}\) and \( {r} = 3 {i} + 2 {j} - 2…

If F⃗=2i^+j^−k^\vec{F} = 2\hat{i} + \hat{j} - \hat{k} and r⃗=3i^+2j^−2k^\vec{r} = 3\hat{i} + 2\hat{j} - 2\hat{k} then the scalar and vector products of F⃗\vec{F} and r⃗\vec{r} have the magnitudes respectively as 10 252\sqrt{5} 5 343\sqrt{4} 4 5105\sqrt{10} 10 222\sqrt{2}

Multiple Choice Options

  • A 10, 2
  • B 5, 3\sqrt 3 3 _
  • C 4, 5\sqrt 5 5 _
  • D 10, 2\sqrt 2 2 _

Step-by-Step Verified Solution

Given, F _ = 2 i ^ + j ^ _ k ^ and r _ = 3 i ^ + 2 j ^ _ 2 k ^ F _ . r _ = 2 ( 3 ) + 2 ( 1 ) + ( _ 2 ) ( _ 1 ) = 6 + 2 + 2 = 10 F _ _ r _ = | i ^ j ^ k ^ 2 1 _ 1 3 2 _ 2 | = i ^ ( _ 2 + 2 ) _ j ^ ( _ 4 + 3 ) + k ^ ( 4 _ 3 ) _ F _ _ r _ = j ^ + k ^ | F _ _ r _ | = 1 2 + 1 2 = 2

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