If vec r ⋅ vec a = vec r ⋅ vec b = vecr ⋅ vecc = 0 for some non-zero vector vec r, then the value of [ vec a vecb vec c] is

Question

If vec r ⋅ vec a = vec r ⋅ vec b = vecr ⋅ vecc = 0 for some non-zero vector vec r, then the value of [ vec a vecb vec c] is (A) 2 (B) 3 (C) 0 (D) None of these

Tardigrade Admin · Accepted Answer

Given, r⋅ a=0 ⇒ r ⊥ a r ⋅ b =0 ⇒ r ⊥ b and r⋅ c=0 ⇒ r ⊥ c ⇒ a, b and c are coplanar ∴ [a b c]=0

Q. If $r \cdot a = r \cdot b = r \cdot c = 0$ for some non-zero vector $r$ , then the value of $[a b c]$ is

2

3

0

None of these

Given, $r \cdot a = 0$
$\Rightarrow r ⊥ a$
$r \cdot b = 0$
$\Rightarrow r ⊥ b$ and $r \cdot c = 0$
$\Rightarrow r ⊥ c$
$\Rightarrow a, b$ and $c$ are coplanar
$∴ [a b c] = 0$

Q. If r⋅a=r⋅b=r⋅c=0 for some non-zero vector r, then the value of [abc] is

2

3

0

None of these

Given, r⋅a=0 ⇒r⊥a r⋅b=0 ⇒r⊥b and r⋅c=0 ⇒r⊥c ⇒a,b and c are coplanar ∴[abc]=0

Q. If $r \cdot a = r \cdot b = r \cdot c = 0$ for some non-zero vector $r$ , then the value of $[a b c]$ is

Given, $r \cdot a = 0$
$\Rightarrow r ⊥ a$
$r \cdot b = 0$
$\Rightarrow r ⊥ b$ and $r \cdot c = 0$
$\Rightarrow r ⊥ c$
$\Rightarrow a, b$ and $c$ are coplanar
$∴ [a b c] = 0$