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Vector Addition

If a⃗=2î+3ĵ...

Question

If $\to a = 2^i + 3^j - 4^k, \to b =^i +^j +^k$ and $\to c = 4^i + 3^k$ , then $| \to a \times (\to b \times \to c) | =$

A

\sqrt{10}

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B

1

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C

2

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D

\sqrt{129}

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Solution

The correct option is D $\sqrt{129}$
$\to a \times (\to b \times \to c)$
$= \to b (\to a . \to c) - \to c (\to a . \to b)$
$= \to b (8 - 12) - \to c (2 + 3 - 4)$
$= - 4 \to b - \to c$
$= - (4 (i + j + k) + 4 i + 3 k)$
$= - (8 i + 4 j + 4 k)$
Now $| - (8 i + 4 j + 7 k) |$
$= \sqrt{64 + 16 + 49}$
$= \sqrt{80 + 49}$
$= \sqrt{129}$

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Similar questions

\to a = 2^i +^j - 3^k, \to b =^i - 2^j +^k

\to c = -^i +^j - 4^k

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

| (\to a \times \to b) \times (\to c \times \to d) |

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

\to a =^i - 2^j - 3^k, \to b = 2^i +^j -^k

\to c =^i + 3^j - 2^k

\to a \times (\to b \times \to c) = p^i + q^j + r^k

p + q + r =

\to a =^i + 2^j + 4^k, \to b = 2^i - 3^j +^k

\to c =^i + 4^j - 4^k

then the vector

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

is orthogonal to

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

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