If a- -k- and b-2-0-k- then the vectors c- satisfying the conditions- i that it is coplanar with a- and b- ii that it is perpendicular to b- and iii that a-c-7- is

Given a⃗= î+ĵ+k̂ b⃗=2î+0ĵ+k̂ Let c = xî+yĵ+zk̂ If a⃗,b⃗,c⃗ are coplanar [a⃗,b⃗,c⃗]=0 [ 1 amp; 1 amp;1; 2 amp; 0 amp; 1; x amp; y amp ...

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Applications Scalar Triple Product

If a⃗=- î+ĵ+k...

Question

If $\to a = -^i +^j +^k$ and $\to b = 2^i + 0^j +^k$ then the vectors $\to c$ satisfying the conditions, (i) that it is coplanar with $\to a$ and $\to b$ (ii) that it is perpendicular to $\to b$ , and (iii) that $\to a . \to c = 7$ , is

- \frac{3}{2}^i + \frac{5}{2}^j + 3^k

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- 3^i + 5^j + 6^k

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- 6^i + 0^j + 5^k

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-^i + 2^j + 2^k

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\to a = -^i +^j +^k

\to b = 2^i + 0^j +^k

\to c

\to a & \to b

\to b

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\to a = -^i +^j +^k

\to b = 2^i + 0^j +^k

\to c

\to a

\to b

\to b

\to a . \to c = 7

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

\to b =^j -^k,

\to c

\to a . \to c = 3

\to a \times \to c = \to b

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

\to c = -^i + 2^i -^k . A

\to a + \to b

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

\to c

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

\to a . \to c = 4

| \to c |^{2}

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