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 A √(14) Projection of v along u=v·u|u| #160; —–(1)Projection of w along u=w·u|u| #160; —–(2) v·w=0 ...

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Byju's Answer

Standard XII

Physics

Acceleration in 2D

Let u⃗, v⃗,...

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

2

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\sqrt{7}

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\sqrt{14}

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14

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Solution

The correct option is A $\sqrt{14}$
Projection of $¯ ¯ ¯ v$ along $¯ ¯ ¯ u = \frac{¯ ¯ ¯ v \cdot ¯ ¯ ¯ u}{| ¯ ¯ ¯ u |}$ -----(1)
Projection of $¯ ¯¯ ¯ w$ along $¯ ¯ ¯ u = \frac{¯ ¯¯ ¯ w \cdot ¯ ¯ ¯ u}{| ¯ ¯ ¯ u |}$ -----(2)
$¯ ¯ ¯ v \cdot ¯ ¯¯ ¯ w = 0$
$| ¯ ¯ ¯ u - ¯ ¯ ¯ v + ¯ ¯¯ ¯ w | = \sqrt{| ¯ ¯ ¯ u |^{2} + | ¯ ¯ ¯ v |^{2} + | ¯ ¯¯ ¯ w |^{2} - 2 ¯ ¯ ¯ u \cdot ¯ ¯ ¯ v - 2 ¯ ¯¯ ¯ w \cdot ¯ ¯ ¯ v + 2 ¯ ¯ ¯ u \cdot ¯ ¯¯ ¯ w}$
$= \sqrt{1 + 4 + 9}$
$= \sqrt{14}$

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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

\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:

\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

and

\to w

be vectors such that

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

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

and

| \to w | = 5,

then

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

Q. Let

\to u

and

\to v

be two unit vectors. If

\to w

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

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is equal to

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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

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