If a⃗=2î+4ĵ+3k̂ and b⃗=î−2ĵ−k̂, and c⃗×a⃗=xî+yĵ+zk̂ for triangle sides a⃗,b⃗,c⃗ taken in order, find y.
Physics · Mixed Chapter
JEE Main Practice

Question

If a⃗=2î+4ĵ+3k̂ and b⃗=î−2ĵ−k̂, and c⃗×a⃗=xî+yĵ+zk̂ for triangle sides a⃗,b⃗,c⃗ taken in order, find y.

G1 Physics · Accepted Answer

Step 1: For a triangle taken consecutively, a⃗+b⃗+c⃗=0 ⇒c⃗=−(a⃗+b⃗). Step 2: c⃗×a⃗=−b⃗×a⃗=a⃗×b⃗. Step 3: The j-component of a⃗×b⃗ is a_z b_x−a_x b_z =3×1−2×(−1)=5. Step 4: Therefore y=5.