Let veca , vecb and veccbe three unit vectors, out of which vectors vecb and vecc are non-parallel. If α and β are the angles which vector a veca makes with vectors vecb and veccrespectively and veca × ( vecb × vecc) = (1/2) vecb,then |α - β|is equal to :

Question

Let veca , vecb and veccbe three unit vectors, out of which vectors vecb and vecc are non-parallel. If α and β are the angles which vector a veca makes with vectors vecb and veccrespectively and veca × ( vecb × vecc) = (1/2) vecb,then |α - β|is equal to : (A) 60° (B) 30° (C) 90° (D) 45°

Tardigrade Admin · Accepted Answer

( veca. vecc) vecb - ( veca. vecb). vecc = (1/2) vecb ∵ vecb vecc are linearly independent ∴ veca. vecc = (1/2) veca . vecb = 0 (All given vectors are unit vectors) ∴ veca hat vecc = 60° veca hat vecb = 90° ∴ |α - β| = 30°

Q. Let $a, b an d c$ be three unit vectors, out of which vectors $b$ and $c$ are non-parallel. If $α$ and $β$ are the angles which vector a $a$ makes with vectors $b an d c$ respectively and $a \times (b \times c) = \frac{1}{2} b$ ,then $∣ α - β ∣$ is equal to :

$6 0^{\circ}$

$3 0^{\circ}$

$9 0^{\circ}$

$4 5^{\circ}$

$(a . c) b - (a . b) . c = \frac{1}{2} b$
$∵ b$ & $c$ are linearly independent
$∴ a . c = \frac{1}{2}$ & $a . b = 0$
(All given vectors are unit vectors)
$∴ a^c = 6 0^{\circ}$ & $a^b = 9 0^{\circ}$
$∴ ∣ α - β ∣ = 3 0^{\circ}$

Q. Let a,bandcbe three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a a makes with vectors bandcrespectively and a×(b×c)=21​b,then ∣α−β∣is equal to :

60∘

30∘

90∘

45∘