Vertices of a triangle are represented by vectors →A=^i−2^j+2^k,→B=2^i+^j−^k and →C=3^i−^j+2^k. Then,
A
Length of side AB is 5 units.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Length of side BC is of length √14 units.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Angle between side AB & BC is θ=cos−1√1419.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Angle between side AB and BC is 30∘.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct options are B Length of side BC is of length √14 units. C Angle between side AB & BC is θ=cos−1√1419. →BA=→OA−→OB ⇒→BA=−^i−3^j+3^k →BC=→OC−→OB ⇒→BC=^i−2^j+3^k |→BA|=√19 and |→BC|=√14 →BA.→BC=|→BA||→BC|cosθ⇒cosθ=→BA.→BCBA.BC cosθ=−1+6+9√14√19=√14√19