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Multiplication with Vectors

Let v = i × ...

Question

Let
$\to v = \to i \times (\to j \times (\to k \times (\to i \times (\to j \times (\to k \times (\to i \times (\to j \times (\to j \times \to k))))))))$ .
Then the value of $| | \to v | |$ is ?

A

0

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B

1

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C

\sqrt{3}

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D

3

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Solution

The correct option is C $1$
$\to v =^i \times (^j \times (^k \times (^i \times (^j \times (^k \times (^i \times (^j \times (^j \times (^k))))))))) \Rightarrow \to v =^i \times (^j \times (^k \times (^i \times (^j \times (^k \times (^i \times (^j \times^i))))))) \Rightarrow \to v =^i \times (^j \times (^k \times (^i \times (^j \times (^k \times (^i \times -^k)))))) \Rightarrow \to v =^i \times (^j \times (^k \times (^i \times (^j \times (^k \times^j))))) \Rightarrow \to v =^i \times (^j \times (^k \times (^i \times (^j \times -^i)))) \Rightarrow \to v =^i \times (^j \times (^k \times (^i \times^k))) \Rightarrow \to v =^i \times (^j \times (^k \times -^j)) \Rightarrow \to v =^i \times (^j \times^i) \Rightarrow \to v =^i \times -^k \Rightarrow \to v =^j S o, ∣ ∣ \to v ∣ ∣ = 1$

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Similar questions

\to v = \to i \times (\to j \times (\to k \times (\to i \times (\to j \times (\to k \times (\to i \times (\to j \times (\to j \times \to k))))))))

Then the value of

∣ ∣ ∣ ∣ \to v ∣ ∣ ∣ ∣

{\to V}_{1} =^i +^j - 2^k, {\to V}_{2} =^i - 2^j +^k, {\to V}_{3} = - 2^i + 2^j +^k

are three vectors. Let

\to V

be a vector such that it can be expressed as a linear combination of

{\to V}_{1}

{\to V}_{2}

\to V {\to V}_{3} = 0

and the projection of the vector

\to V

^i -^j +^k

6 \sqrt{3}

\to V = λ (^i + 3^j - 4^k)

then find the absolute value of

λ

Q. The value of

\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{i} \times \hat{j}),

is
(a) 0
(b) −1
(c) 1
(d) 3

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

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

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

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

be three vectors. A vector

\to v

in the plane of

\to a

\to b

, whose projection on

\to c

\frac{1}{\sqrt{3}}

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