Let A be vector parallel to line of intersection of planes P_1 and P_2 through origin. P_1 is parallel to the vectors 2j+3k and 4j-3k and P_2 is parallel to j-k and 3i+3j then the angle between vector A and 2i+j-2k is

Admiddevadxvi

Admiddevadxvi

Answered question

2023-02-21

Let A be vector parallel to line of intersection of planes P 1 and P 2 through origin. P 1 is parallel to the vectors 2 j ^ + 3 k ^ and 4 j ^ 3 k ^ and P 2 is parallel to j ^ k ^ and 3 i ^ + 3 j ^ then the angle between vector A and 2 i + j 2 k ^

Answer & Explanation

Jakob Howell

Jakob Howell

Beginner2023-02-22Added 4 answers

Let vector A O be parallel to line of planes P 1 and P 2 through origin.
Normal to plane p 1 is
n 1 = [ ( 2 j + 3 k ) × 4 j ^ 3 k ^ ) ] = 18 i ^
Normal to plane p 2 is
n 2 = ( j ^ k ^ ) × ( 3 i ^ + 3 j ^ ) = 3 i ^ 3 j ^ 3 k ^
So, O A is parallel to ± ( n 1 × n 2 ) = 54 j ^ 54 k ^
Angle between 54 ( j ^ k ^ ) and ( 2 i ^ + j ^ 2 k ^ ) is
cos θ = ± ( 54 + 108 3.54 2 ) = ± 1 2 θ = π 4 , 3 π 4

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