Let u- v- w- be such that - u- - - 1- - v- - - 2- - w- - - 3 - If the projection v- along u- is equal to that of w- along u- and v- w- are perpendicular to each other - then - u-v- - w- - equals

The correct option is A √(14) Given, #160; |u⃗|=1 and |v⃗|=2,|w⃗|=3 and, v⃗·u⃗=w⃗·u⃗ v⃗·u⃗=ω⃗·u⃗ or, v⃗·ω⃗=0 Now, |u⃗ v⃗+w ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Let u⃗, v...

Question

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

\sqrt{14}

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\sqrt{7}

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Solution

The correct option is A $\sqrt{14}$
Given,
$| \to u | = 1$ and $| \to v | = 2, | \to w | = 3$
and, $\to v \cdot \to u = \to w \cdot \to u$

$\to v \cdot \to u = \to ω \cdot \to u$

or, $\to v \cdot \to ω = 0$
Now, $| \to u - \to v + \to w |$
Squaring, $| \to u |^{2} + {\to v |}^{2} + | \to w |^{2} - 2 \to u \cdot \to v - 2 \to v \cdot \to ω$
$+ 2 \to u \cdot \to w$
$\Rightarrow 1 + 4 + 9 - 2 \to u \cdot \to v + 2 \to u \cdot \to v$ -0
$\Rightarrow 14$
$| \to u - \to v + \to w | = \sqrt{14}$
option $A = \sqrt{14}$

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Similar questions

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

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is equal to that of

\to w

along

\to u

and

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are perpendicular to each other, then

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

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Q. Let

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be such that

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

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is equal to that of

\to w

along

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and

\to v, \to w

are perpendicular to each other then

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equals:

\to u, \to v, \to w

be such that

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

If the projection of

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along

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Let →u, →v, →w be such that |→u| = 1, |→v| = 2, |→w| = 3 . If the projection →v along →u is equal to that of →w along →u and →v, →w are perpendicular to each other , then |→u→v+→w| equals

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