→a=^i−2^j+3^k
→b=3^i−2^j+^k
and θ is the angle between →a and →b.
|→a|=√12+(−2)2+(3)2
=√1+4+9=√14
|→b|=√32+(−2)2+12
=√9+4+1=√14
Now, |→a|∣∣→b∣∣ sin θ=∣∣→a×→b∣∣
sin θ=∣∣→a×→b∣∣∣∣→a∣∣∣∣→b∣∣=∣∣
∣
∣∣^i^j^k1−233−21∣∣
∣
∣∣√14 √14
= ∣∣4^i+8^j+4^k∣∣14
= √16+64+1614=√9614=4√614=27√6