A unit vector parallel to the intersection of the planes vecr ⋅( hati- hatj+ hatk)=5 and vecr ⋅(2 hati+ hatj-3 hatk)=4 is

Question

A unit vector parallel to the intersection of the planes vecr ⋅( hati- hatj+ hatk)=5 and vecr ⋅(2 hati+ hatj-3 hatk)=4 is (A) (2 hati+5 hatj-3 hatk/√38) (B) (2 hati-5 hatj+3 hatk/√38) (C) (-2 hati-5 hatj-3 hatk/√38) (D) (-2 hati+5 hatj-3 hatk/√38)

Tardigrade Admin · Accepted Answer

hata=± ( vecn1 × vecn2/| vecn1 × vecn2|)=± (2 hati+5 hatj+3 hatk/√38) (where vecn1 and vecn2 are normal to the planes)

Q. A unit vector parallel to the intersection of the planes $r \cdot (\hat{i} - \hat{j} + \hat{k}) = 5$ and $r \cdot (2 \hat{i} + \hat{j} - 3 \hat{k}) = 4$ is

$\frac{2 i ^ + 5 j ^ - 3 k ^}{38}$

$\frac{2 i ^ - 5 j ^ + 3 k ^}{38}$

$\frac{- 2 i ^ - 5 j ^ - 3 k ^}{38}$

$\frac{- 2 i ^ + 5 j ^ - 3 k ^}{38}$

$\overset{a}{^} = \pm \frac{n _{1} \times n _{2}}{∣ n _{1} \times n _{2} ∣} = \pm \frac{2 i ^ + 5 j ^ + 3 k ^}{38}$
(where $n_{1}$ and $n_{2}$ are normal to the planes)

Q. A unit vector parallel to the intersection of the planes r⋅(i^−j^​+k^)=5 and r⋅(2i^+j^​−3k^)=4 is

38​2i^+5j^​−3k^​

38​2i^−5j^​+3k^​

38​−2i^−5j^​−3k^​

38​−2i^+5j^​−3k^​