As →p,→q,→r are coplanar,
∣∣
∣∣a+1aaaa+1aaaa+1∣∣
∣∣=0
R1→R1+R2+R3
⇒∣∣
∣∣3a+13a+13a+1aa+1aaaa+1∣∣
∣∣=0
⇒(3a+1)∣∣
∣∣111aa+1aaaa+1∣∣
∣∣=0
C2→C2−C1 , C3→C3−C1
⇒(3a+1)∣∣
∣∣100a10a01∣∣
∣∣=0
⇒3a+1=0⇒a=−13
→p=13(2^i−^j−^k),→q=13(−^i+2^j−^k),
→r=13(−^i−^j+2^k)
→r×→q=19∣∣
∣
∣∣^i^j^k−1−12−12−1∣∣
∣
∣∣
→r×→q=19(−3^i−3^j−3^k)
=−13(^i+^j+^k)
|→r×→q|2=13
→p.→q=19(−2−2+1)=−13
3(→p.→q)2−λ|→r×→q|2=0⇒13−λ×13=0
⇒λ=1