let a¯,b¯ and c¯ be three vectors, then a¯×(b¯×c¯)=(a¯×b¯)×c¯ if

a→×(b→×c→)=(a→×b→)×c→⇒(a→⋅c→)b→−(b→⋅c→)a→=(c→⋅a→)b→−(b→⋅a→)c→⇒(b→⋅c→)a→=(b→⋅a→)c→ [∵a→⋅c→=c→⋅a→]⇒(b→⋅c→)a→−(b→⋅a→⋅)c→=0→⇒b→×(a→×c→)=0→

let a¯,b¯ and c¯ be three vectors, then a¯×(b¯×c¯)=(a¯×b¯)×c¯ if

a→×(b→×c→)=(a→×b→)×c→⇒(a→⋅c→)b→−(b→⋅c→)a→=(c→⋅a→)b→−(b→⋅a→)c→⇒(b→⋅c→)a→=(b→⋅a→)c→ [∵a→⋅c→=c→⋅a→]⇒(b→⋅c→)a→−(b→⋅a→⋅)c→=0→⇒b→×(a→×c→)=0→

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

let $\bar{a}, \bar{b} and \bar{c}$ be three vectors, then $\bar{a} \times (\bar{b} \times \bar{c}) = (\bar{a} \times \bar{b}) \times \bar{c}$ if

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\bar{a} \times \bar{b} = \bar{c} \times a$

$\bar{b} \times (\bar{a} \times \bar{c}) = \bar{0}$

$\bar{a} \cdot \bar{c} = \bar{b} \times \bar{c}$

$\bar{b} \times \bar{c} = \bar{a} \times \bar{b}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{b}) \times \vec{c}$
$\begin{array}{l} \Rightarrow (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{b} \cdot \vec{c}) \vec{a} = (\vec{c} \cdot \vec{a}) \vec{b} - (\vec{b} \cdot \vec{a}) \vec{c} \\ \Rightarrow (\vec{b} \cdot \vec{c}) \vec{a} = (\vec{b} \cdot \vec{a}) \vec{c} [∵ \vec{a} \cdot \vec{c} = \vec{c} \cdot \vec{a}] \\ \Rightarrow (\vec{b} \cdot \vec{c}) \vec{a} - (\vec{b} \cdot \vec{a} \cdot) \vec{c} = \vec{0} \\ \Rightarrow \vec{b} \times (\vec{a} \times \vec{c}) = \vec{0} \end{array}$