Let a, b, c be three vectors such that $[a\,b\,c] = 2.$ If $r = l(b \times c) + m(c \times a) + n(a \times b)$ is perpendicular to $a + b + c,$ then the value of $(l + m + n)\,\,{\text{ is }}$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

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Analyzing +4 | -1

Let a, b, c be three vectors such that

[a\,b\,c] = 2.

r = l(b \times c) + m(c \times a) + n(a \times b)

is perpendicular to

a + b + c,

then the value of

(l + m + n)\,\,{\text{ is }}

View answer and explanation

Correct option: C

Option C (0) is correct because the condition r is perpendicular to (a + b + c) leads to l + m + n = 0.

Practice All Chapter MCQs →

\vec r\cdot\vec a = \vec r\cdot\vec b = \vec r\cdot\vec c = 0

\vec r,

\left[ {\vec a\vec b\vec c} \right],

\frac{{x - 3}}{2} = \frac{{y - 2}}{3} = \frac{{z - 1}}{{ - 1}}

\frac{{x + 3}}{2} = \frac{{y - 6}}{1} = \frac{{z - 5}}{3},

\mathbf{\vec a} = \widehat \mathbf{i} - \mathbf{\hat k},\;\mathbf{\vec b} = x\widehat \mathbf{i} + \widehat \mathbf{j} + \left( {1 - x} \right)\mathbf{\hat k}

\mathbf{\vec c} = y\widehat \mathbf{i} + x\widehat \mathbf{j} + \left( {1 + x - y} \right)\mathbf{\hat k}.

\left[ {\mathbf{\vec a},\;\mathbf{\vec b},\;\mathbf{\vec c}} \right]

\vec{a}, \vec{b}

((\vec{a} \times \vec{b}) \times \vec{a}) \cdot((\vec{b} \times \vec{a}) \times \vec{b})

a \cdot(a \times b)=

\mathbf{r}=\mathbf{b}+\lambda \mathbf{c}