Find the altitude of a parallelopiped determined by a- b- c- if yhe base a- - b- and if a- - - - - - k- b- - 2- - 4- - k- - c- - - - - -3k-

Given, a⃗=î+ĵ+k̂; b⃗=2î+4ĵ k̂ and c⃗=î+ĵ+3k̂ and the base is a parallelogram determined by a⃗ and b⃗ The altitude of a parallelopiped is given by ...

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Applications of Dot Product

Find the alti...

Question

Find the altitude of a parallelopiped determined by $\to a, \to b, \to c$ if yhe base $\to a, & \to b$ and if $\to a =^i +^j +^k; \to b = 2^i + 4^j -^k & \to c =^i +^j + 3^k$ .

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\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

\to c^{'} = 2^i +^j -^k

\to a, \to b, \to c

\to b

\to c

(\to a, \to b, \to c

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

\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

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

\sqrt{78}

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

\to c = 4^i + 3^k

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

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

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

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

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

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