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

a⃗ =i+4j+2k ; b⃗ =3i 2j+7k d⃗ is perpendicular to both a⃗ and b⃗ ∴ #160;d⃗ is parallel of a⃗× #160;b⃗ a⃗×b⃗ =(i+4j+ ...

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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 $\to b, \to d = 15$ .

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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 b + \to c)

\to a

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

\to c =^i +^k

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

\to d

¯ d

\to c

\to d

\to a = 10, \to b = 1

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