If r and s arenon-zero constant vectors and the scalar b is chosen such that | r +b s | is minimum, then the value of |b s |^ 2 +| r +b s |^ 2 is equal to

Correct answer: D. | r |^ 2 For minimum value | r +b s |=0 . Let r and s are anti-parallel so b s =- r |b s |^ 2 +| r +b s |^ 2 =|- r |^ 2 +| r - r |^ 2 =| r |^ 2

BITSAT 2020

Exam: BITSAT
Year: 2020
Subject: Mathematics
Chapter: Vector Algebra

BITSAT 2020 · Mathematics · Vector Algebra

If r and s arenon-zero constant vectors and the scalar b is chosen...

\vec{r}

and

\vec{s}

arenon-zero constant vectors and the scalar

b

is chosen such that

|\vec{r}+b \vec{s}|

is minimum, then the value of

|b \vec{s}|^{2}+|\vec{r}+b \vec{s}|^{2}

is equal to

Options

A $2|\vec{r}|^{2}$
B $|\vec{r}|^{2} / 2$
C $3|\vec{r}|^{2}$
D $|\vec{r}|^{2}$

Correct answer

D. $|\vec{r}|^{2}$

Step-by-step solution

For minimum value

|\vec{r}+b \vec{s}|=0

. Let

\vec{r}

and

\vec{s}

are anti-parallel so

b \vec{s}=-\vec{r}\therefore|b \vec{s}|^{2}+|\vec{r}+b \vec{s}|^{2}=|-\vec{r}|^{2}+|\vec{r}-\vec{r}|^{2}=|\vec{r}|^{2}

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