Given two vectors A = 3 i ^ + j ^ − 2 k ^ and B = i ^ − 3 j ^ + 4 k ^ . Match the following quantities. List - I List - II (P) Scalar product A ⋅ B (1) 1/2∣ A × B ∣ (Q) Vector product A × B (2) −

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Given two vectors A = 3 i ^ + j ^ ​ − 2 k ^ and B = i ^ − 3 j ^ ​ + 4 k ^ . Match the following quantities. List - I List - II (P) Scalar product A ⋅ B (1) 1/2∣ A × B ∣ (Q) Vector product A × B (2) − 8 (R) Angle between A and B (3) cos − 1 ( 14 ​ 26 ​ − 8 ​ ) (S) Area of the triangle formed by A and B as adjacent sides (4) − 2 i ^ − 14 j ^ ​ − 10 k ^

TestHub · Accepted Answer

The scalar product is A ⋅ B = ( 3 ) ( 1 ) + ( 1 ) ( − 3 ) + ( − 2 ) ( 4 ) = 3 − 3 − 8 = − 8 . The vector product is A × B = ( − 2 i ^ − 14 j ^ ​ − 10 k ^ ) . The angle θ between them is given by cos θ = ∣ A ∣∣ B ∣ A ⋅ B ​ . ∣ A ∣ = 14 ​ , ∣ B ∣ = 26 ​ . So θ = cos − 1 ( 14 ​ 26 ​ − 8 ​ ) . The area of the triangle formed by A and B as adjacent sides is 2 1 ​ ∣ A × B ∣.

List - I	List - II
(P) Scalar product $A \cdot B$	(1) $1/2∣ A \times B ∣$
(Q) Vector product $A \times B$	(2) $- 8$
(R) Angle between $A$ and $B$	(3) $cos^{- 1} (\frac{- 8}{14 26})$
(S) Area of the triangle formed by $A$ and $B$ as adjacent sides	(4) $- 2 \hat{i} - 14 \hat{j} - 10 \hat{k}$

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