If the vectors `hati-2hatj+hatk,ahati-5hatj+3hatkand5hati-9hatj+4hatk` are coplanar, then the value of a is …………..

Options

A. 3
B. `-3`
C. 2
D. `-2`

Answer

C

Explanation

Let `vec(P)=hat(i)-2hat(j)+hat(k),vec(q)=ahati-5hatj+3hatk,vec(r)=5hati-9hatj+4hatk`
`:'vec(p),vec(q)andvec(r)` are coplanar,
`:.[vec(p)vec(q)vec(r)]=0`
`implies|{:(1,-2,1),(a,-5,3),(5,-9,4):}|=0`
`implies1(-20+27)+2(4a-15)+1(-9a+25)=0`
`7+8a-30-9a+25=0`
`-a+2=0`
`a=2`