If P = 2 i ^ + 3 j ^ − k ^ and Q = i ^ − 2 j ^ + 4 k ^ , calculate the scalar product P ⋅ Q .

The scalar product (dot product) of two vectors P = P x i ^ + P y j ^ + P z k ^ and Q = Q x i ^ + Q y j ^ + Q z k ^ is given by P ⋅ Q = P x Q x + P y Q y + P z Q z . Substituting the given components: P ⋅ Q = ( 2 ) ( 1 ) + ( 3 ) ( − 2 ) + ( − 1 ) ( 4 ) = 2 − 6 − 4 = − 8 .

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PhysicsVectorsMultiplication of vectorsEasy2 minai-gemini

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If $P = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $Q = \hat{i} - 2 \hat{j} + 4 \hat{k}$ , calculate the scalar product $P \cdot Q$ .

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The scalar product (dot product) of two vectors $P = P_{x} \hat{i} + P_{y} \hat{j} + P_{z} \hat{k}$ and $Q = Q_{x} \hat{i} + Q_{y} \hat{j} + Q_{z} \hat{k}$ is given by $P \cdot Q = P_{x} Q_{x} + P_{y} Q_{y} + P_{z} Q_{z}$ . Substituting the given components: $P \cdot Q = (2) (1) + (3) (- 2) + (- 1) (4) = 2 - 6 - 4 = - 8$ .

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

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