The magnitude of the projection of the vector 2 i ^ + j ^ + k , on the vector perpendicular to the plane containing the vectors i ^ + j ^ + k ^ and i ^ + 2 j ^ + 3 k ^ , is

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The magnitude of the projection of the vector 2 i ^ + j ^ ​ + k , on the vector perpendicular to the plane containing the vectors i ^ + j ^ ​ + k ^ and i ^ + 2 j ^ ​ + 3 k ^ , is

TestHub · Accepted Answer

The perpendicular vector is ​ i ^ 1 1 ​ j ^ ​ 1 2 ​ k ^ 1 3 ​ ​ = i ^ − 2 j ^ ​ + k ^ the required projection = ∣ i ^ − 2 j ^ ​ + k ^ ∣ ( 2 i ^ + j ^ ​ + k ^ ) ⋅ ( i ^ − 2 j ^ ​ + k ^ ) ​ = 1 2 + ( − 2 ) 2 + 1 2 ​ 2 − 2 + 1 ​ = 6 ​ 1 ​

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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