Let u - v - w be such that - u -1- - v - -2- w -3- If the projection of 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 D √(14) Let the angles between nbsp; u, nbsp;v nbsp;be nbsp; α nbsp;; nbsp; v, nbsp;w nbsp;be nbsp; ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let u , v ,...

Question

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

\sqrt{14}

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\sqrt{7}

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2

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14

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Solution

The correct option is D $\sqrt{14}$
Let the angles between $\to u, \to v$ be $α$ ; $\to v, \to w$ be $β$ and between $\to w, \to u$ be $γ$
Here, $2 cos α = 3 cos γ$ and $β = 90^{o}$
$∣ ∣ \to u - \to v + \to w ∣ ∣ = \sqrt{u^{2} + v^{2} + w^{2} + 2 (\to u \cdot \to w) - 2 (\to u \cdot \to v) - 2 (\to v \cdot \to w)} = \sqrt{14 + 6 c o s γ - 4 cos α - 0}$
$= \sqrt{14}$

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Similar questions

Q. Let

\to u, \to v

, and

\to w

be such that

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

and

| \to w | = 3.

If the projection of

\to v

along

\to u

is equal to that

\to w

along

\to u

, and

\to v

and

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are perpendicular to each other, then |

\to u

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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 the projection of

\to w

along

\to u

and

\to v, \to w

are perpendicular to each other, then

∣ ∣ \to u - \to v + \to w ∣ ∣ =

Q. 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| =

Q. Let

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and

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be such that

| u | = 1, | v | = 3

and

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Let →u,→v,→w be such that |→u|=1,|→v|=2,|→w|=3. If the projection of →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 D √14Let the angles between →u,→v be α ; →v,→w be β and between →w,→u be γHere, 2cosα=3cosγ and β=90o∣∣→u−→v+→w∣∣=√u2+v2+w2+2(→u⋅→w)−2(→u⋅→v)−2(→v⋅→w)=√14+6cosγ−4cosα−0=√14

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