Find the equation of line of intersection of planes r- 3i-j-k-1 and r- 3i-4j-2k-2

→r⃗(3î ĵ+k̂) = 1 ...(1) r⃗ (3î+4ĵ 2k̂) = 2 ...(2) Let r⃗ = xî+yĵ+zk̂ ∴ we get (1) as #160; 3x y+z = 1 ...(3) ∴ we get (2) a # ...

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Byju's Answer

Standard XII

Mathematics

Family of Planes Passing through the Intersection of Two Planes

Find the equa...

Question

Find the equation of line of intersection of planes $\to r \cdot (3 \to i - \to j + \to k) = 1$ and $\to r \cdot (3 \to i + 4 \to j - 2 \to k) = 2$

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Solution

$\to \to r (3^i -^j +^k) = 1 . . . (1)$
$\to r - (3^i + 4^j - 2^k) = 2 . . . (2)$
Let $\to r = x^i + y^j + z^k$
$∴$ we get (1) as
$3 x - y + z = 1 . . . (3)$
$∴$ we get (2) a
$3 x + 4 y - 2 z = 2 . . . (4)$
Subtracting (3) and (4), we get
$- 5 y + 32 = - 1$
$∴ 5 y - 3 z - 1 = 0$
is the Equation of line of intersection

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Find the equation of line of intersection of planes →r⋅(3→i−→j+→k)=1 and →r⋅(3→i+4→j−2→k)=2

→→r(3^i−^j+^k)=1...(1)→r−(3^i+4^j−2^k)=2...(2)Let →r=x^i+y^j+z^k∴ we get (1) as 3x−y+z=1...(3)∴ we get (2) a 3x+4y−2z=2...(4)Subtracting (3) and (4), we get −5y+32=−1∴5y−3z−1=0is the Equation of line of intersection

Find the equation of line of intersection of planes $\to r \cdot (3 \to i - \to j + \to k) = 1$ and $\to r \cdot (3 \to i + 4 \to j - 2 \to k) = 2$