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Vector Addition

Let a =2 î+ĵ-...

Question

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i + \to j$ . If $\to c$ is a vector such that $\to a . c = | \to c |, | \to c - \to a | = 2 \sqrt{2}$ and the angle between $\to a \times \to b$ and $\to c i s 30^{\circ}$ , then $| (\to a \times \to b) \times \to c |$

A

\frac{2}{3}

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B

\frac{3}{2}

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C

2

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D

3

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Solution

The correct option is B $\frac{3}{2}$
$(\to a \times \to b) \times \to c = (\to a . \to c) \to b - (\to a . \to b) \to c c o s 30^{\circ} = \frac{(\to a \times \to b) . \to c}{| \to a \times \to b | | \to c |}$

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Similar questions

\to a = 2^i +^j - 2^k a n d \to b =^i +^j .

\to c

is a vector such that

\to a . \to c = | \to c |, | \to c - \to a | = 2 \sqrt{2}

and the angle between

(\to a \times \to b) a n d \to c i s 30^{\circ}, t h e n | (\to a \times \to b) \times \to c |

\to a = 2^i +^j - 2^k a n d \to b =^i +^j .

\to c

is a vector such that

\to a . \to c = | \to c |, | \to c - \to a | = 2 \sqrt{2}

and the angle between

(\to a \times \to b) a n d \to c i s 30^{\circ}, t h e n | (\to a \times \to b) \times \to c |

\to a = 2^i +^j - 2^k, \to b =^i +^j

^c

is a vector such that

\to a . \to c = | \to c |, | \to a + \to c | = 2 \sqrt{3}

and angle between

\to a \times \to b

\to c

30^{\circ}

| (\to a \times \to b) . \to c | =

\to a = 2^i +^j - 2^k

\to b =^i +^j .

\to c

is a vector such that

\to a \cdot \to c = ∣ ∣ \to c ∣ ∣,

∣ ∣ \to c - \to a ∣ ∣ = 2 \sqrt{2}

and the angle between

(\to a \times \to b)

\to c

\frac{π}{6},

then the value of

∣ ∣ ∣ (\to a \times \to b) \times \to c ∣ ∣ ∣

\to a = 2^i +^j - 2^k

\to b =^i +^j .

\to c

be a vector such that

| \to c - \to a | = 3, | (\to a \times \to b) \times \to c | = 3

and the angle between

\to c

\to a \times \to b

30^{\circ} .

\to a \cdot \to c

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