Consider three vectors v-1- v-2 and v-3 such that v-1 - v-2 - v-3 where v-1 - a-i -i- v-2 - a-j -j v-3 - a-k -k- a- is non zero vector- then

The correct option is C a⃗. j = 0 Let a⃗=ai+bj+ck Then v⃗_⃗1⃗=(a⃗× i)× i =a⃗ ai ...(i)Similarly #160; v⃗_⃗2⃗=a⃗ bj ...(ii) v⃗_⃗3 ...

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Formation of a Differential Equation from a General Solution

Consider thre...

Question

Consider three vectors ${\to v}_{1}, {\to v}_{2}$ and ${\to v}_{3}$ such that
${\to v}_{1} = {\to v}_{2} - {\to v}_{3}$ where ${\to v}_{1} = (\to a \times ˆ i) \times ˆ i$ ,
${\to v}_{2} = (\to a \times ˆ j) \times ˆ j$ & ${\to v}_{3} = (\to a \times ˆ k) \times ˆ k$ .
( $\to a$ is non zero vector), then

\to a . ˆ j = 0

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\to a . ˆ i = 0

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\to a . ˆ k = 0

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{\to v}_{1} . {\to v}_{2} = (\to a . ˆ j)^{2}

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Solution

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¯ a, ¯ b, ¯ c

_{1},_{2},_{3}

_{1} = \frac{\to b \times \to c}{[\to a \to b \to c]},_{2} = \frac{\to c \times \to a}{[\to a \to b \to c]},_{3} = \frac{\to a \times \to b}{[\to a \to b \to c]}

\to a

\to b

\to a = ˆ i - 2 ˆ j + 3 ˆ k

\to b = ˆ i + 2 ˆ j - ˆ k

ˆ i . (ˆ j \times ˆ k) + ˆ j . (ˆ i \times ˆ k) + ˆ k . (ˆ i \times ˆ j)

\to P = ˆ i + ˆ j + ˆ k; \to q = 2 ˆ i + 4 ˆ j - ˆ k

\to r = 2 ˆ i + 4 ˆ j + 3 ˆ k

\to p, \to q

\to r

\to r

\to r \times \to b = \to r \times \to c

\to b = ˆ i + 2 ˆ j + ˆ k

\to c = 3 ˆ i + 2 ˆ k

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