Let U-2-k-W-3k- if V is a unit vector-then the maximum value of -U-V-W- is

The correct option is C √(59) [U,V,W]=U.(V×W) =|U| |V×W| =U×W from the question. =[î nbsp; amp;ĵ nbsp; amp; k̂ 2 amp ...

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Standard XII

Mathematics

Definition of Function

Let U=2î+ĵ-...

Question

Let $\to U = 2^i +^j -^k, - \to W =^i + 3^k$ , if $\to V$ 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{59}

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\sqrt{60}

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Solution

The correct option is C $\sqrt{59}$
$[\to U, \to V, - \to W] = \to U . (\to V \times - \to W)$
$= ∣ ∣ ∣ \to U ∣ ∣ ∣ ∣ ∣ ∣ \to V \times - \to W ∣ ∣ ∣$
$= \to U \times - \to W$ from the question.
$= ⎡ ⎢ ⎣ \begin{matrix} ^i & ^j & ^k 2 & 1 & - 1 1 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦$
$=^i (3 - 0) -^j (6 + 1) +^k (0 - 1)$
$= 3^i - 7^j -^k$
$∴ ∣ ∣ ∣ \to V \times - \to W ∣ ∣ ∣ = \sqrt{3^{2} + 7^{2} + 1} = \sqrt{59}$
$∣ ∣ ∣ \to U ∣ ∣ ∣ = 1$ (given)
$\Rightarrow [\to U, \to V, - \to W] \leq \sqrt{59}$

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Let →U=2^i+^j−^k,−→W=^i+3^k, if →V is a unit vector,then the maximum value of [→U,→V,−→W] is

Let $\to U = 2^i +^j -^k, - \to W =^i + 3^k$ , if $\to V$ is a unit vector,then the maximum value of $[\to U, \to V, - \to W]$ is