Let u- v- and w- be vectors such that u- - v- - w- - 0- If -u- - 3- -v- - 4 and -w- - 5- then u- v- - v- w- - w- u- is

Since, u⃗ + v⃗ + w⃗ = 0⃗ ⇒ |u⃗ + v⃗ + w⃗|^2 = 0 ⇒ |u⃗|^2 + |v⃗|^2 + |w⃗|^2 + 2(u⃗. v⃗ + v⃗. w⃗ + w⃗.u⃗) = 0 ⇒ 9 + 16 + 25 + 2 (u⃗. v⃗ + v⃗. w⃗ + w⃗.u⃗) = 0 ⇒u⃗. ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let u⃗, v⃗ an...

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

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-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 such that

| \to u | = 1, | \to v | = 2, | \to w | = 3.

If the projection of

\to v

along

\to u

is equal to that of

\to w

along

\to u

and vectors

\to v, \to w

are perpendicular to each other then

| \to u - \to v + \to w |

equals

Q. Let

\to u, \to v, \to w

be such that

| \to u | = 1, | \to v | = 2, | \to w | = 3

. If the projection

\to v

along

\to u

is equal to that of

\to w

along

\to u

and

\to v, \to w

are perpendicular to each other then

| \to u - \to v + \to w |

equals:

Q. Let

\to u, \to v, \to w

be such that

| \to u | = 1, | \to v | = 2, | \to w | = 3

. If the projection of

\to v

along

\to u

is equal to that of

\to w

along

\to u

and

\to v, \to w

are perpendicular to each other, then

| \to u - \to v + \to w |

equals

Q. Let

\to u

\to v

\to w

be such that

| \to u |

= 1,

| \to v |

= 2,

| \to w |

= 3 . If the projection

\to v

along

\to u

is equal to that of

\to w

along

\to u

and

\to v

\to w

are perpendicular to each other , then

| \to u \to v + \to w |

equals

Q. 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 the value of

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

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

The correct option is B -25Since, →u+→v+→w=→0⇒|→u+→v+→w|2=0⇒|→u|2+|→v|2+|→w|2+2(→u.→v+→v.→w+→w.→u)=0⇒9+16+25+2(→u.→v+→v.→w+→w.→u)=0⇒→u.→v+→v.→w+→w.→u=−25

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