If A-1-1-1 and C-0-1-1 are given vectors- then vector B- satisfying the equation A-B-C- and A-B-3 is -

Let B⃗ =xî yĵ +zk̂ According to question A⃗ .B⃗ =3 ⇒ x+y+z=3 Also, A⃗×B⃗ =C⃗ ⇒ i amp; j amp; k 1 amp; 1 amp; 1 ...

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Equation of Plane Containing Two Lines

If A⃗=1,1,1...

Question

If $\to A = (1, 1, 1)$ and $\to C = (0, 1, - 1)$ are given vectors, then vector $\to B$ satisfying the equation $\to A \times \to B = \to C$ and $\to A . \to B = 3$ is $-$

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Solution

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\to A = (1, 1, 1), \to C = (0, 1, - 1)

\to B

\to A \times \to B = \to C

\to A . \to B = 3

\to A

\to C

\to B

\to A \times \to B = \to C a n d \to A . \to B = 3

\to a, \to b, \to c

\to b, \to c

(\to a, \to b) = α, (\to a, \to c) = β

\to a \times (\to b \times \to c) = \frac{\to b + \to c}{2}

c o s (α + β) =

\to a, \to b, \to c

\to a . \to b = 0

\to a + \to b = \to c

\to a = \to i + \to j + \to k, \to c = \to j - \to k

\to b

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

\to a . \to b = 3

\to b

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