Let P R → = 3 i ^ + j ^ - 2 k ^ and S Q → = i ^ - 3 j ^ - 4 k ^ represent the diagonals of the parallelogram P Q R S . If P T → = 2 i ^ - j ^ + k ^ is another vector, then the volume (in cubic units) of the parallelepiped formed by the vectors P T → , P Q → and P S → is

Question

Let P R → = 3 i ^ + j ^ - 2 k ^ and S Q → = i ^ - 3 j ^ - 4 k ^ represent the diagonals of the parallelogram P Q R S . If P T → = 2 i ^ - j ^ + k ^ is another vector, then the volume (in cubic units) of the parallelepiped formed by the vectors P T → , P Q → and P S → is,

MARKS App · Accepted Answer

Here, P Q → + P S → = P R → P Q → - P S → = S Q → ⇒ P Q → = 1 2 P R → + S Q → ⇒ P Q → = 2 i ^ - j ^ - 3 k ^ Also, P S → = 1 2 P R → - S Q → = i ^ + 2 j ^ + k ^ Volume of parallelepiped = P T → P Q → P S → = 2 - 1 1 2 - 1 - 3 1 2 1 = 2 5 + 1 5 + 1 5 = 20 cubic units

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