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 # ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

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 $\to r \cdot (3 \to i + 4 \to j - 2 \to k) = 2$

Open in App

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

Suggest Corrections

Similar questions

Q. The line of intersection of the planes

\to r . (3 \to i - \to j + \to k) = 1

and

\to r . (\to i + 4 \to j - 2 \to k) = 2

is parallel to the vector

Q. The vector equation of the plane through the point

\to i + 2 \to j - \to k

and

⊥

to the line of intersection of the plane

\to r . (3 \to i - \to j + \to k) = 1

and

\to r . (\to i + 4 \to j - 2 \to k) = 2

Q. If

\to r = 3 \to i + 2 \to j - 5 \to k

\to a = 2 \to i - \to j + \to k

\to b = \to i + 3 \to j - 2 \to k

and

\to c = - 2 \to i + \to j - 3 \to k

such that

\to r = λ \to a + μ \to b + ν \to c

then

Q. Find the vector and Cartesian equations of the plane passing through the points with position vectors

3 \to i + 4 \to j + 2 \to k, 2 \to i - 2 \to j - \to k

, and

7 \to i + \to j + \to k

The shortest distance between the lines $\to r = 3 \to i + 5 \to j + 7 \to k + λ (\to i + 2 \to j + \to k) a n d \to r = - \to i - \to j - \to k + μ (7 \to i - 6 \to j + \to k) i s$

Join BYJU'S Learning Program

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 $\to r \cdot (3 \to i + 4 \to j - 2 \to k) = 2$