Find the vector u- v when u- 3-4-6 - and v- 0-1-1 -

The correct option is C [ 2, 3,3 ] Given, u=[3,4,6] and v=[0,1,1] Let w=u× v ∴ w_x=u_yv_z u_zv_y #160; #160; #160; #160; ...

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Cardinal Properties

Find the vect...

Question

Find the vector $u \times v$ when $u = [3, 4, 6]$ and $v = [0, 1, 1]$ .

[6, 2, - 1]

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[- 3, 1, 1]

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[- 2, - 3, 3]

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[0, 4, 6]

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Solution

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\to u

\to v

(\to u . \to v)^{2} + | \to u \times \to v |^{2} - | \to u |^{2} | \to v |^{2}

¯ ¯ ¯ u

¯ ¯ ¯ v

{(¯ ¯ ¯ u . ¯ ¯ ¯ v)}^{2} + {(¯ ¯ ¯ u \times ¯ ¯ ¯ v)}^{2} = {∣ ∣ ¯ ¯ ¯ u ∣ ∣}^{2} {∣ ∣ ¯ ¯ ¯ v ∣ ∣}^{2}

{(1 + ¯ ¯ ¯ u)}^{2} + {(1 + ¯ ¯ ¯ v)}^{2} = {(1 - ¯ ¯ ¯ u . ¯ ¯ ¯ v)}^{2} + {∣ ∣ ¯ ¯ ¯ u + ¯ ¯ ¯ v + (¯ ¯ ¯ u \times ¯ ¯ ¯ v) ∣ ∣}^{2}

\vec{u,} \vec{v} and \vec{w}

\vec{u} + \vec{v} + \vec{w} = \vec{0} .

|\vec{u}| = 3, |\vec{v}| = 4 and |\vec{w}| = 5,

\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} .

u + v

u = (3, 4, - 2)

v = (0, - 4, 0)

u

v

u = (2, 0)

v = (- 3, 1)

w = - u - 2 v

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