If the vectors -2-k-2-5-pk- and are 5-9-4k- are coplanar- then find the value of p

We know that if 3 vectors a⃗, vecb, c⃗ are co planar, then [a⃗, b⃗, c⃗] = 0 ∴ #160;[ 1 amp; 2 amp;1; 2 amp; 5 amp;p; ...

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Cross Product of Two Vectors

If the vector...

Question

If the vectors $^i - 2^j +^k, 2^i - 5^j + p^k$ and are $5^i - 9^j + 4^k$ are coplanar, then find the value of $p$

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\to r = (2^i + 9^j + 13^k) + t (^i + 2^j + 3^k)

\to r = (- 3^i + 7^j + p^k) + s (-^i + 2^j - 3^k)

- (^j +^k), 4^i + 5^j + λ^k, 3^i + 9^j + 4^k

- 4^i + 4^j + 4^k

λ

\to a

2^i -^j +^k,^i + 2^j - 3^k

3^i + a^j + 5^k

2^i -^j +^k,^i + 2^j - 3^k

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a

\to A, \to B & \to C

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

\to C = m^i + 2^j +^k

m

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