If the vectors A = 2 i ^ + 3 j ^ − k ^ and B = 4 i ^ − 2 j ^ + n k ^ are perpendicular to each other, what is the value of n ?

Two vectors A and B are perpendicular if their dot product is zero, i.e., A ⋅ B = 0 . Given A = 2 i ^ + 3 j ^ − k ^ and B = 4 i ^ − 2 j ^ + n k ^ . ( 2 ) ( 4 ) + ( 3 ) ( − 2 ) + ( − 1 ) ( n ) = 0 ⟹ 8 − 6 − n = 0 ⟹ 2 − n = 0 ⟹ n = 2 .

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PhysicsVectorsMultiplication of vectorsMedium2 minai-gemini

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If the vectors $A = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $B = 4 \hat{i} - 2 \hat{j} + n \hat{k}$ are perpendicular to each other, what is the value of $n$ ?

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Two vectors $A$ and $B$ are perpendicular if their dot product is zero, i.e., $A \cdot B = 0$ . Given $A = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $B = 4 \hat{i} - 2 \hat{j} + n \hat{k}$ . $(2) (4) + (3) (- 2) + (- 1) (n) = 0 ⟹ 8 - 6 - n = 0 ⟹ 2 - n = 0 ⟹ n = 2$ .

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: ai-gemini

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