If →a=^i+^j−^k,→b=−^i+2^j+2^k & →c=−^i+2^j−^k, find a unit vectors normal to the vectors →a+→b and →b+→c.
A
−^i−2^j+6^k√40
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
−^i−2^j+6^k√41
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
^i−2^j+6^k√41
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
−^i+2^j+6^k√41
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B−^i−2^j+6^k√41 →a+→b=3^j+^k →b+→c=−2^i+4^j+^k Since we need a unit vector perpendicular to the vectors (3^j+^k) and (−2^i+4^j+^k), we take their cross products. (3^j+^k)×(−2^i+4^j+^k)=6^k+3^i−2^j−4^i =−^i−2^j+6^k Unit vector thus becomes −^i−2^j+6^k√41