Ex 10.5, 3 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra

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Ex 10.5, 3 (Supplementary NCERT) Find if the vectors + , 3 + + 2 and + 3 are coplanar.Three vectors , , are coplanar if [ " " " " ] = 0 Let = + = 3 + + 2 = + 3 [ " " " " ] = | 8(1& 1&1@3&1&2@1&" " & 3)| 0 = 1[(1 3) (" " 2) ] ( 1)[(3 3) (1 2) ] + 1[(3 " " ) (1 1) ] 0 = 1 [ 3 2" " ]+1[ 9 2]+1[3" " 1] 0 = 3 2 11 + 3 1 0 = 3 11 1 + 3 2 0 = 15 + 15 = = 15 Therefore, , , are coplanar if = 15