Let →a,→b and →c be three non-zero vectors such that no two of them are collinear and (→a×→b)×→c=13∣∣∣→b∣∣∣∣∣→c∣∣→a. If θ is the angle between vectors →b and →c, then a value of sinθ is
A
23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
−2√33
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2√23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
−√23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B2√23 (→a×→b)×→c=−c×(→c×→b)=−[(→c.→b)→a−(→c.→a)→b]=(→c.→a)→b−(→c.→b)→a≡13∣∣→b∣∣|→c||→a|−(→c.→b)=13∣∣→b∣∣|→c|−|→c|∣∣→b∣∣cosθ=13∣∣→b∣∣|→c|cosθ=13sinθ=2√23Hence,optionCiscorrectanswer.