Let a- - - - - b- - - - - - k- and c- be a vector such that a-c- - b- - 0- and a- - c- - 4- then -c-2 is equal to

The correct option is A 192 a⃗×c⃗ = ⃗b⃗ (a⃗×c⃗) ×a⃗ = b⃗×a⃗ ⇒ (a⃗×c⃗)×a⃗ = a⃗×b⃗ ⇒ (a⃗ . a⃗)c⃗ (c⃗ . a⃗) a⃗ = a⃗×b⃗ ⇒ 2c⃗ 4 ...

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Byju's Answer

Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

Let a⃗ = î ...

Question

Let $\to a =^i -^j, \to b =^i +^j +^k$ and $\to c$ be a vector such that $\to a \times \to c + \to b = \to 0$ and $\to a . \to c = 4$ , then $| \to c |^{2}$ is equal to

\frac{19}{2}

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\frac{17}{2}

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Solution

The correct option is A $\frac{19}{2}$
$\to a \times \to c = \to - b$
$(\to a \times \to c) \times \to a = - \to b \times \to a$
$\Rightarrow (\to a \times \to c) \times \to a = \to a \times \to b$
$\Rightarrow (\to a . \to a) \to c - (\to c . \to a) \to a = \to a \times \to b$
$\Rightarrow 2 \to c - 4 \to a = \to a \times \to b$
Now $\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 0 1 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = -^i -^j + 2^k$
So, $2 \to c = 4^i - 4^j -^i -^j + 2^k$
$= 3^i - 5^j + 2^k$
$\Rightarrow \to c = \frac{3}{2}^i - \frac{5}{2}^j +^k$
$| \to c | = \sqrt{\frac{9}{4} + \frac{25}{4} + 1} = \sqrt{\frac{38}{4}} = \sqrt{\frac{19}{2}}$
$| \to c |^{2} = \frac{19}{2}$ .

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Similar questions

Q. Let

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

and

\to c

be a vector such that

\to a \times \to c + \to b = \to 0

and

\to a \cdot \to c = 4

, then

| \to c |^{2}

is equal to:

Q. Let

\to a =^i +^j +^k, \to c =^j -^k

and a vector

\to b

be such that

\to a \times \to b = \to c

and

\to a \cdot \to b = 3.

Then

| \to b |

equals :

Q. Let

\to a =^j -^k

and

\to c =^i -^j -^k

. Then vector

\to b

satisfying

\to a \times \to b + \to c = \to 0

and

\to a \cdot \to b = 3

Q. Let

\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 |

is equal to

Q. Let

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

and

\to b =^i +^j

. If

\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)

and

\to c

30^{0}

, then

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

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Let →a=^i−^j,→b=^i+^j+^k and →c be a vector such that →a×→c+→b=→0 and →a.→c=4, then |→c|2 is equal to

Let $\to a =^i -^j, \to b =^i +^j +^k$ and $\to c$ be a vector such that $\to a \times \to c + \to b = \to 0$ and $\to a . \to c = 4$ , then $| \to c |^{2}$ is equal to