The correct option is C 3√30
We have →a1=3^i+8^j+3^k →b1=3^i−^j+^k
→a2=−3^i−7^j+6^k and →b2=−3^i+2^j+4^k
Now, b1×b2=∣∣
∣
∣∣^i^j^k3−11−324∣∣
∣
∣∣=−6^i−15^j+3^k
∣b1×b2∣=√62+152+32=3√30
a1−a2=6^i+15^j−3^k
Therefore shortest distance between both the lines is
d=∣(a1−a2)×(b1×b2)∣b1×b2∣∣=62+152+323√30=3√30