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Applications of Dot Product

Let u , v and...

Question

Let $\to u, \to v$ and $\to w$ be vectors such that $\to u + \to v + \to w = \to 0 .$ If $| \to u | = 3, | \to v | = 4$ and $| \to w | = 5,$ then $\to u . \to v + \to v . \to w + \to w . \to u$ is

A

47

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B

-25

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C

25

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Solution

The correct option is B -25
Since, $\to u + \to v + \to w = \to 0 \Rightarrow | \to u + \to v + \to w |^{2} = 0 \Rightarrow | \to u |^{2} + | \to v |^{2} + | \to w |^{2} + 2 (\to u . \to v + \to v . \to w + \to w . \to u) = 0 \Rightarrow 9 + 16 + 25 + 2 (\to u . \to v + \to v . \to w + \to w . \to u) = 0 \Rightarrow \to u . \to v + \to v . \to w + \to w . \to u = - 25$

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Similar questions

\to u, \to v

\to w

be vectors such that

\to u + \to v + \to w = \to 0 .

| \to u | = 3, | \to v | = 4

| \to w | = 5,

\to u . \to v + \to v . \to w + \to w . \to u

u, v

w

be vectors such that

u + v + w = 0

| u | = 3, | v | = 4

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u . v + v . w + w . u

\vec{u,} \vec{v} and \vec{w}

be vectors such

\vec{u} + \vec{v} + \vec{w} = \vec{0} .

|\vec{u}| = 3, |\vec{v}| = 4 and |\vec{w}| = 5,

\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} .

\to u

\to v

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\to w

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\to w + (\to w \times \to u) = \to v

, then maximum value of

2 | (\to u \times \to v) . \to w |

Let u,v and w be vectors such that u+v+w. If |u|=3,|v|=4 and ||w|=5. Then the value of u.v+v.w+w.u is

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