DR's of PQ are 7λ−7,−λ+5,−2λ ‌PQ⟂L ‌⇒(7λ−7)7+(−1)(−λ+5)+(−2λ)(−2)=0 ‌⇒49λ−49+λ−5+4λ=0 ‌⇒54λ−54=0⇒λ=1 ‌P(10,1,−3)‌ and ‌R(3,−2,1) ‌
→
PQ
=−4
^
j
+2
^
k
,
→
QR
=−7
^
i
+
^
j
+2
^
k
, ‌
→
PR
=−7
^
i
−3
^
j
+4
^
k
‌
→
PQ
â‹…
→
QR
=0⇒‌ right angle at ‌Q ‌⇒ar(△PQR)=‌
1
2
×PQ×QR ‌=‌
1
2
×√20×√54 ‌=‌
1
2
×2×3(√5×√6) ‌=3√30 ‌⇒‌ Option ‌(1)‌ is correct ‌