Let p-2-3-k- and q-2-k- be two vectors- If a vector r-k- is perpendicular to each of the vectors p-q and p-q- and -r-3- then - is equal to

R =√(3)(p+q)×(p q)|(p+q)×(p q)| =√(3) i amp;j nbsp; amp;k nbsp; nbsp;3 amp; 5 amp;2 nbsp; 1 amp;1 nbsp; amp;0 nbsp; |(p+q)×(p ...

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Summary

Let p=2î+3ĵ+k...

Question

Let $\to p = 2^i + 3^j +^k$ and $\to q =^i + 2^j +^k$ be two vectors. If a vector $\to r = α^i + β^j + γ^k$ is perpendicular to each of the vectors $(\to p + \to q)$ and $(\to p - \to q),$ and $∣ ∣ \to r ∣ ∣ = \sqrt{3},$ then $| α | + | β | + | γ |$ is equal to

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

\to q =^i - 2^j +^k

5 \sqrt{3}

\to q

\to p

\to q

^i + p^j +^k, 2^i + 3^j + q^k

(p, q) = ?

P, Q, R

_{1} = 3^i - 2^j -^k,_{2} =^i + 3^j + 4^k

_{3} = 2^i +^j - 2^k

O

P

O Q R

P

(1, 0, 1), (1, - 2, 1)

(0, 1, - 2) .

\to a = α^i + β^j + γ^k

\to a

P

(^i + 2^j + 3^k)

\to a \cdot (^i +^j + 2^k) = 2.

(α - β + γ)^{2}

α^i +^j +^k,^i + β^j +^k,^i +^j + λ^k (α, β, γ \neq 1)

\frac{1}{1 - α} + \frac{1}{1 + β} + \frac{1}{1 - γ}

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