The vector is expressible as

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The vector r\mathbf{r} is expressible as (1) r=[rbc]2[abc]a+[rca]2[abc]b+[rab]2[abc]c\mathbf{r} = \frac{[\mathbf{r}\mathbf{b}\mathbf{c}]}{2[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{a} + \frac{[\mathbf{r}\mathbf{c}\mathbf{a}]}{2[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{b} + \frac{[\mathbf{r}\mathbf{a}\mathbf{b}]}{2[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{c} (2) r=2[rbc][abc]a+2[rcb][abc]b+2[rab][abc]c\mathbf{r} = \frac{2[\mathbf{r}\mathbf{b}\mathbf{c}]}{[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{a} + \frac{2[\mathbf{r}\mathbf{c}\mathbf{b}]}{[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{b} + \frac{2[\mathbf{r}\mathbf{a}\mathbf{b}]}{[\mathbf{a}\mathbf{b}\mathbf{c}]} \mathbf{c} (3) r=1[abc]([rbc]a+[rca]b+[rab]c)\mathbf{r} = \frac{1}{[\mathbf{a}\mathbf{b}\mathbf{c}]} ([\mathbf{r}\mathbf{b}\mathbf{c}]\mathbf{a} + [\mathbf{r}\mathbf{c}\mathbf{a}]\mathbf{b} + [\mathbf{r}\mathbf{a}\mathbf{b}]\mathbf{c}) (4) None of the above

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