If overrightarrow{a}, overrightarrow{b}, over | vedclass

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(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.This can be rewritten as $\

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(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.This can be rewritten as $\overrightarrow{r} = \overrightarrow{a} + p(\overrightarrow{b} - \overrightarrow{a}) + q(\overrightarrow{c} - \overrightarrow{a})$.Let $\overrightarrow{u} = \overrightarrow{b} - \overrightarrow{a}$ and $\overrightarrow{v} = \overrightarrow{c} - \overrightarrow{a}$.Then the equation becomes $\overrightarrow{r} = \overrightarrow{a} + p\overrightarrow{u} + q\overrightarrow{v}$.Since $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are non-coplanar,the vectors $\overrightarrow{u}$ and $\overrightarrow{v}$ are non-collinear.An equation of the form $\overrightarrow{r} = \overrightarrow{a} + p\overrightarrow{u} + q\overrightarrow{v}$ represents a plane passing through the point with position vector $\overrightarrow{a}$ and parallel to the vectors $\overrightarrow{u}$ and $\overrightarrow{v}$.

Column-$I$	Column-$II$
$(a)$ Gymnosperms	$(p)$ Trimerous flowers
$(b)$ Monocots	$(q)$ Absence of flowers
$(c)$ Dicots	$(r)$ Primitive flowers
$(d)$ Pteridophytes	$(s)$ Tetramerous or pentamerous flowers

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three non-coplanar vectors,then the vector equation $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$ represents a :

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Match the following columns:

Column-$I$ Column-$II$

$(a)$ Gymnosperms $(p)$ Trimerous flowers

$(b)$ Monocots $(q)$ Absence of flowers

$(c)$ Dicots $(r)$ Primitive flowers

$(d)$ Pteridophytes $(s)$ Tetramerous or pentamerous flowers

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