Vector ` vec c` is perpendicular to vectors ` vec a=(2,-3,1)a n d vec b=(1,-2,3)` and satisfies the condition ` vec x cdot( hat i+2 hat j-7 hat k)=10.` Then vector ` vec c` is equal to a.`(7,5,1)` b. `-7,-5,-1` c. `1,1,-1` d. none of these

Options

A. 7,5,1
B. (-7, -5, -1)
C. 1,1,-1
D. none of these

Answer

a

Explanation

Let `vecc = lambda (veca xx vecb)`.
Hence, ` lambda(veca xx vecb) . (hati + 2hatj -7hatk) =10`
` Rightarrow lambda|{:(2,-3,1),(1,-2,3), (1,2,-7):}|=10`
`or lambda = -1`
` Rightarrow vecc = - (veca xx vecb)` \