Given p- 2-4-1- q- - 3-1-2- r- - 5-5- 4- Then P-Q- and Q-R- are

The correct option is A CollinearGiven vector p⃗=(2, 4,1)=2î 4ĵ+k̂ q⃗=(3, 1,2)=3î ĵ+2k̂ r⃗=(5,5,4)=5î+5ĵ+4k̂ P⃗Q⃗=Q⃗ P⃗ P⃗Q⃗=3î ĵ+2k̂ ( ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Equations

Given p⃗= 2...

Question

Given $\to p = (2, - 4, 1), \to q = (3, - 1, 2), \to r = (5, 5, 4)$ . Then $\to P Q$ and $\to Q R$ are

Collinear

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Equal

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Non-collinear

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Negative of each other

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Solution

The correct option is A Collinear
Given vector
$\to p = (2, - 4, 1) = 2^i - 4^j +^k$
$\to q = (3, - 1, 2) = 3^i -^j + 2^k$
$\to r = (5, 5, 4) = 5^i + 5^j + 4^k$
$\to P Q = \to Q - \to P$
$\to P Q = 3^i -^j + 2^k - (2^i - 4^j +^k)$
$\to P Q = 3^i -^j + 2^k - 2^i + 4^j -^k$
$\to P Q =^i + 3^j +^k$

$\to Q R = \to R - \to Q$
$\to Q R = 5^i + 5^j + 4^k - (3^i -^j + 2^k)$
$\to Q R = 5^i + 5^j + 4^k - 3^i +^j - 2^k$
$\to Q R = 2^i + 6^j + 2^k = 2 (^i + 3^j +^k)$
$\to Q R = λ (\to P Q)$
Hence collinear

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Given →p=(2,−4,1),→q=(3,−1,2),→r=(5,5,4). Then →PQ and →QR are

Given $\to p = (2, - 4, 1), \to q = (3, - 1, 2), \to r = (5, 5, 4)$ . Then $\to P Q$ and $\to Q R$ are