Let a-4-2k- b-3-2-7k- and c-2-4k- Find a vector d- which is perpendicular to both a- and b- and c-d-15-

Consider the problem #160;Given, #160; [ a⃗ =î +4ĵ +2k̂ #160;; #160;; b⃗ =3î 2ĵ +7k̂ #160;; #160;; c⃗ =2î ĵ ...

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Applications of Cross Product

Let a⃗=î+4ĵ...

Question

Let $\to a =^i + 4^j + 2^k, \to b = 3^i - 2^j + 7^k$ and $\to c = 2^i -^j + 4^k$ . Find a vector $\to d$ which is perpendicular to both $\to a$ and $\to b$ , and $\to c \cdot \to d = 15$ .

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Solution

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\to a =^i + 4^j + 2^k, \to b = 3^i - 2^j + 7^k

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

\to d

\to a

\to b

\to c \cdot \to d = 15

\to a =^i + 4^j + 2^k, \to b = 3^i - 2^j + 7^k

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

\to p

\to a

\to b

\to p \cdot \to c = 18.

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

\to c = 6^i - 3^j +^k

\to d

\to a

\to b

\to c . \to d = 2

\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 = 4^i + 5^j -^k, \to b =^i - 4^j + 5^k, and \to c = 3^i -^j -^k

\to d

\to c

\to b

\to d

\to a = 21

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