V-2-k- and w- - - u- is a unit vector then the maximum value of -u- v- w- is

The correct option is C √(2) v⃗×w⃗= i amp; #160; ĵ amp;k̂ #160; 2 amp; #160; 1 amp; 1 #160; 1 amp;0 #160; amp;0 =ĵ ...

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Byju's Answer

Standard XII

Mathematics

Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

v⃗=2î+ĵ-k̂ an...

Question

$\to v = 2^i +^j -^k$ and $\to w =^i$ , $\to u$ is a unit vector then the maximum value of $[\to u$ $\to v$ $\to w]$ is

- 1

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\sqrt{10} + \sqrt{6}

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\sqrt{2}

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\sqrt{60}

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Solution

The correct option is C $\sqrt{2}$
$\to v \times \to w = ∣ ∣ ∣ ∣ ∣ \begin{matrix} i & ^j & ^k 2 & 1 & - 1 1 & 0 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ =^j -^k$

$= [\to u \to v \to w] = \to v - \to v \times \to w$
$= | \to u | | \to v \times \to w | cos θ$
$\leq ∣ ∣ \to U ∣ ∣ ∣ ∣ \to U \times \to w ∣ ∣$
$\leq \sqrt{2}$

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Similar questions

$\to V = 2^i +^j -^k$ and $\to W =^i + 3^k$ . If $\to U$ is a unit vector, then the maximum value of the scalar triple product $[\to U \to V \to W]$ is

\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 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 .

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

and

| \to w | = 5,

then

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

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→v=2^i+^j−^k and →w=^i , →u is a unit vector then the maximum value of [→u →v →w] is

The correct option is C √2→v×→w=∣∣ ∣ ∣∣i^j^k21−1100∣∣ ∣ ∣∣=^j−^k=[→u→v →w]=→v−→v×→w=|→u||→v×→w|cosθ≤ ∣∣→U∣∣∣∣→U×→w∣∣≤ √2

$\to v = 2^i +^j -^k$ and $\to w =^i$ , $\to u$ is a unit vector then the maximum value of $[\to u$ $\to v$ $\to w]$ is