Let a -2 -2 k- and b - Let c be a vector such that - c - a -3- a - b - c -3 and the angle between c and a -b be 30- Then a - c is equal to-A- 25-8B- 5C- 2 1D- 8

The correct option is C 2 nbsp; nbsp;|a|^2= 4+1+4=9 and a×b=2 î 2 ĵ+ k̂ ⇒ |a×b|=9 Also |c a|=3 ⇒ |c|^2+|a|^2 2 c·a=9 ⇒ |c|^2 2 nbsp;c·a=0 ⋯ (1) Also, ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a =2 î+ĵ-...

Question

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i +^j .$ Let $\to c$ be a vector such that $| \to c - \to a | = 3, | (\to a \times \to b) \times \to c | = 3$ and the angle between $\to c$ and $\to a \times \to b$ be $30^{\circ} .$ Then $\to a \cdot \to c$ is equal to:

\frac{25}{8}

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2

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5

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\frac{1}{8}

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Solution

The correct option is B $2$
$| \to a |^{2} = 4 + 1 + 4 = 9$
$and \to a \times \to b = 2^i - 2^j +^k$
$\Rightarrow | \to a \times \to b | = 9$
Also
$| \to c - \to a | = 3$
$\Rightarrow | \to c |^{2} + | \to a |^{2} - 2 \to c \cdot \to a = 9$
$\Rightarrow | \to c |^{2} - 2 \to c \cdot \to a = 0 \dots (1)$
$Also, | (\to a \times \to b) \times \to c | = 3$
$\Rightarrow | \to a \times \to b | | \to c | sin 30^{\circ} = 3$
$\Rightarrow 3 | \to c | \times \frac{1}{2} = 3$
$\Rightarrow | \to c | = 2$
$From (1), \to c \cdot \to a = \to a \cdot \to c = 2$

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Similar questions

Q. Let

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

and

\to b =^i +^j .

Let

\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

and

\to a \times \to b

30^{\circ} .

Then

\to a \cdot \to c

is equal to:

Let $a = 2^i +^j - 2^k, b =^i +^j$ and $c$ be a vector such that $| c - a | = 3, | (a \times b) \times c | = 3$ and the angle between $c$ and $a \times b$ is $30^{\circ}$ . Then, $a \cdot c$ is equal to