The magnitude of the projection of the vector 2 i ^ + 3 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 ^ + 3 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

​ ∣ ( i ^ + j ^ ​ + k ^ ) × ( i ^ + 2 j ^ ​ + 3 k ^ ) ∣ ∣ ( 2 i ^ + 3 j ^ ​ + k ^ ) ⋅ {( i ^ + j ^ ​ + k ^ ) × ( i ^ + 2 j ^ ​ + 3 k ^ )} ∣ ​ = ∣ i ^ + j ^ ​ + k ^ ∣ ∣ ( 2 i ^ + 3 j ^ ​ + k ^ ) ⋅ ( i ^ − 2 j ^ ​ + k ^ ) ∣ ​ = 1 2 + ( − 2 ) 2 + 1 2 ​ ∣2 − 6 + 1∣ ​ = 6 ​ 3 ​ = 2 3 ​ ​ ​

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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