If r is a unit vector satisfying r × a = b ,| a |=2 and | b |=√3, then one such r =

Question

If r is a unit vector satisfying r × a = b ,| a |=2 and | b |=√3, then one such r = (A) (1/4)[2 a +( b × a )] (B) (1/4)[ a -(2 b × a )] (C) (1/3)[ a -( b × a )] (D) (1/4)[ a -( b × a )]

Tardigrade Admin · Accepted Answer

We have, r × a = b | r × a |=| b | | r || a | sin θ=| b | sin θ=(| b |/| a |)=(√3/2) [⋅| r |=1,| a |=2,| b |=√3] ∴ θ=60° ( r × a ) × a = b × a ( r . a ) a -| a |2 r = b × a r =(1/| a |2)[( a ⋅ r ) a - b × a ] r =(1/4)((| a | r | cos θ) a - b × a ) ⇒ r =(1/4)( a -( b × a ))

Q. If $r$ is a unit vector satisfying $r \times a = b, ∣ a ∣ = 2$ and $∣ b ∣ = 3$ , then one such $r =$

$\frac{1}{4} [2 a + (b \times a)]$

$\frac{1}{4} [a - (2 b \times a)]$

$\frac{1}{3} [a - (b \times a)]$

$\frac{1}{4} [a - (b \times a)]$

Q. If r is a unit vector satisfying r×a=b,∣a∣=2 and ∣b∣=3​, then one such r=

41​[2a+(b×a)]

41​[a−(2b×a)]

31​[a−(b×a)]

41​[a−(b×a)]

We have, r×a=b ∣r×a∣=∣b∣ ∣r∣∣a∣sinθ=∣b∣ sinθ=∣a∣∣b∣​=23​​[⋅∣r∣=1,∣a∣=2,∣b∣=3​] ∴θ=60∘ (r×a)×a=b×a (r.a)a−∣a∣2r=b×a r=∣a∣21​[(a⋅r)a−b×a] r=41​((∣a∥r∣cosθ)a−b×a) ⇒r=41​(a−(b×a))

Q. If $r$ is a unit vector satisfying $r \times a = b, ∣ a ∣ = 2$ and $∣ b ∣ = 3$ , then one such $r =$

$\frac{1}{4} [2 a + (b \times a)]$

$\frac{1}{4} [a - (2 b \times a)]$

$\frac{1}{3} [a - (b \times a)]$

$\frac{1}{4} [a - (b \times a)]$