Find a- b-c- if a- - 2- - - - 3k- b- - - - 2- - k- and c- - 3- - - - 2k-

(b × c) = ( i+2j+k) × (3i+j+2k) , which implies (b × c) = (4 1)i + (3+2)j + ( 1 6)k = 3i+5j 7k a.(b × c) = (2i+j+3k).(3i+5j 7k) = 6+5 21 = 10. ...

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Addition and Subtraction in Unit Vector Notation

Find a⃗· b⃗...

Question

Find $\to a \cdot (\to b \times \to c)$ , if $\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k$ and $\to c = 3^i +^j + 2^k .$

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Solution

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

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

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

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

\to b = 3^i + 2^j +^k

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

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

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

\to a = 3^j - 2^j + 7^k, \to b = 5^i +^j - 2^k

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

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

\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

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

\sqrt{78}

\to A = 2^i - 3^j + 7^k, \to B =^i + 2^j

\to C =^j -^k .

\to A \cdot (\to B \times \to C) .

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