If the vectors a =2 i +3 j - k , b =4 i - j +3 k and c = p i + j - k are coplanar, then | a c |=

Step-by-step solution

a =2 i +3 j - k , b =4 i - j +3 k , c = p i + j - k a , b & c are coplanar aligned & a( b c )=[ a , b , c ]=0 & | array ccc 2 & 3 & -1 4 & -1 & 3 p & 1 & -1 array | & 2(1-3)-3(-4-3 p)-1(4+p)=0 & -4+12+9 p-4-p=0 & 8 p=-6 p= -3 4 8 p=-4 p=- 1 2 aligned aligned & Now, a c = | array ccc i & j & k 2 & 3 & -1 - 1 2 & 1 & -1 array | & a c =-2 i + 5 2 j + 7 2 k & | a c |= 4+ 25 4 + 49 4 = 90 4 = 3 10 2 aligned