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Applications of Cross Product

Let A = 2i ...

Question

Let $\to A = 2 ˆ i + ˆ k,$ $\to B = ˆ i + ˆ j + ˆ k$ and $\to c = 4 ˆ i - 3 ˆ j + 7 ˆ k$ .determine a vector $\to R$ satisfying $\to R \times \to B = \to C \times \to B$ and $- \to R . \to A = 0$ .

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Solution

$\begin{matrix} \to A = 2 ˆ i + ˆ k \to B = ˆ i + ˆ j + ˆ k \to C = x ˆ i + y ˆ j + 2 ˆ k \to R = x ˆ i + y ˆ j + 2 ˆ k \to R \times \to B = \to C \times \to B (x ˆ i + y ˆ j + 2 ˆ k) \times (ˆ i + ˆ j + ˆ k) = (4 ˆ i - 3 ˆ j + 7 ˆ k) \times (ˆ i + ˆ j + ˆ k) ˆ i (y - z) - ˆ j (x - z) + ˆ k (x - y) = - 10 ˆ i + 3 ˆ j + 7 ˆ k y - z = - 10 z - x = 3 x - y = 7 \to R \times \to A = 0 2 x + z = 0 z - x = 3 - + - - --------- - 3 x = 3 x = 1, y = 8, z = 4 ∴ \to R = ˆ i + 8 ˆ j + 4 ˆ k \end{matrix}$

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Similar questions

A = 2 i + k, B = i + j + k

C = 4 i - 3 j + 7 k

, then a vector

r

which satisfies

R \times B = C \times B

R . A = 0

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

\to C = 4^i - 3^j + 7^k

.Determine a vector

\to R

\to R . \to A = 0

\to R \times \to B = \to C \times \to B

¯ ¯ ¯ a = 2 ¯ i + ¯ ¯ ¯ k, ¯ ¯ b = ¯ i + ¯ j + ¯ ¯ ¯ k, ¯ ¯ c = 4 ¯ i - 3 ¯ j + 7 ¯ ¯ ¯ k

, then the vector

¯ ¯ ¯ r

¯ ¯ ¯ r \times ¯ ¯ b = ¯ ¯ c \times ¯ ¯ b

¯ ¯ ¯ r . ¯ ¯ ¯ a = 0

¯ ¯ ¯ a = 2 ¯ i + ¯ ¯ ¯ k, ¯ ¯ b = ¯ i + ¯ j + ¯ ¯ ¯ k, ¯ ¯ c = 4 ¯ i - 3 ¯ j + 7 ¯ ¯ ¯ k,

then the vector

¯ ¯ ¯ r

¯ ¯ ¯ r \times ¯ ¯ b = ¯ ¯ c \times ¯ ¯ b

¯ ¯ ¯ r . ¯ ¯ ¯ a = 0

\to a =^j -^k; \to c =^i -^j -^k

. Then the vector

\to b

\to a \times \to b + \to c = 0

\to a . \to b

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