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 ^

Question

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      ^

Jakob Howell · Accepted Answer

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

Let A → be vector parallel to line of intersection of planes P 1 and...

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