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Matrix Definition and Representation

If →a=2î+ĵ-...

Question

If $\to a = 2^i +^j - 3^k$ and $\to b = 3^i +^j + 5^k$ , calculate $\to a \times \to b$ .

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Solution

$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 1 & - 3 3 & 1 & 5 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$= (5 - (- 3))^i - (10 - (- 9))^j + (2 - 3)^k$
$= 8^i - 19^j -^k$

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

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

\to r = x \to a + y \to b + z \to c

Q. Find the scalar and vector products of two vectors,

a = (3^i - 4^j + 5^k)

b = (- 2^i +^j - 3^k)

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

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

\to A \times \to B

\to A = 3^i -^j + 3^k

\to B = - 2^i + 3^j + 4^k

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

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

∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣

.

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