Let veca and vecb be two vectors such that | veca|=1 and veca ⋅( vecb ×( veca × vecb))=8. If the angle between veca and vecb is textcosec-1 √2, then magnitude of vecb is

Question

Let veca and vecb be two vectors such that | veca|=1 and veca ⋅( vecb ×( veca × vecb))=8. If the angle between veca and vecb is textcosec-1 √2, then magnitude of vecb is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Q. Let $a$ and $b$ be two vectors such that $∣ a ∣ = 1$ and $a \cdot (b \times (a \times b)) = 8$ . If the angle between $a$ and $b$ is $cosec^{- 1} 2$ , then magnitude of $b$ is

$a \cdot (b \times (a \times b)) = a b (a \times b) = ∣ a \times b ∣$
$\Rightarrow ∣ a ∣^{2} ∣ b ∣^{2} sin^{2} θ = 8$
$\Rightarrow ∣ b ∣ = 4$

Q. Let a and b be two vectors such that ∣a∣=1 and a⋅(b×(a×b))=8. If the angle between a and b is cosec−12​, then magnitude of b is

a⋅(b×(a×b))=ab(a×b)=∣a×b∣ ⇒∣a∣2∣b∣2sin2θ=8 ⇒∣b∣=4

Q. Let $a$ and $b$ be two vectors such that $∣ a ∣ = 1$ and $a \cdot (b \times (a \times b)) = 8$ . If the angle between $a$ and $b$ is $cosec^{- 1} 2$ , then magnitude of $b$ is

$a \cdot (b \times (a \times b)) = a b (a \times b) = ∣ a \times b ∣$
$\Rightarrow ∣ a ∣^{2} ∣ b ∣^{2} sin^{2} θ = 8$
$\Rightarrow ∣ b ∣ = 4$