JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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Analyzing +4 | -1

If the vectors

\vec{a}, \vec{b}, \vec{c}

are non-coplanar und

l, m, n

are distinct scalars such that

[l \vec{a}+m \vec{b}+n \vec{c} \,\,l \vec{b}+m \vec{c}+n \vec{a} \,\,l \vec{c}+m \vec{a}+n \vec{b}]=0

then

View answer and explanation

Correct option: B

l+m+n=0

Option B (

l+m+n=0

) is correct because the determinant equation simplifies to

(l+m+n)(l^2+m^2+n^2-l m-m n-n l)=0

, and since

l, m, n

are distinct,

l+m+n=0

More Questions from SCALAR TRIPLE PRODUCT

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\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}