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Addition of Vectors

ABC is any tr...

Question

$A B C$ is any triangle and $D, E, F$ are the middle points of its sides $B C, C A, A B$ respectively. Express the vectors $- - \to C F$ and $- - \to B E$ as linear combination of the vectors $- - \to A B$ and $- - \to A C$

A

- - \to B E = \frac{1}{2} - - \to A C - - - \to A B; - - \to C F = \frac{1}{2} - - \to A B - - - \to A C

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B

- - \to B E = \frac{1}{2} - - \to A C + - - \to A B; - - \to C F = \frac{1}{2} - - \to A B + - - \to A C

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C

- - \to C F = \frac{1}{2} - - \to A C - - - \to A B; - - \to B E = \frac{1}{2} - - \to A B - - - \to A C

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D

- - \to C F = \frac{1}{2} - - \to A C + - - \to A B; - - \to B E = \frac{1}{2} - - \to A B + - - \to A C

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Solution

The correct option is A $- - \to B E = \frac{1}{2} - - \to A C - - - \to A B; - - \to C F = \frac{1}{2} - - \to A B - - - \to A C$
$- - \to C A + - - \to A F = - - \to C F$
$\Rightarrow - - - \to A C + \frac{1}{2} - - \to A B = - - \to C F$
Similarly $- - \to A E + - - \to B A = - - \to B E$
$\Rightarrow \frac{1}{2} - - \to A C - - - \to A B = - - \to B E$

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Δ = 0

Δ

can be written as product of two determinants.

e

e_{1}

are the eccentricities of a hyperbola and its conjugate, then

\frac{1}{e^{2}} + \frac{1}{e_{1}^{2}}

\frac{1}{12}

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\frac{1}{17}

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\frac{1}{α}

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