# Current Affairs JEE Main & Advanced

## Equation of Planes Bisecting Angle Between Two Given Planes

Category : JEE Main & Advanced

Equations of planes bisecting angles between the planes ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}}=0$ and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z+d=0$ are $\frac{{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}}}{\sqrt{(a_{1}^{2}+b_{1}^{2}+c_{1}^{2})}}=$ $\pm \frac{{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z+{{d}_{2}}}{\sqrt{(a_{2}^{2}+b_{2}^{2}+c_{2}^{2})}}$.

(i) If angle between bisector plane and one of the plane is less than ${{45}^{o}}$, then it is acute angle bisector, otherwise it is obtuse angle bisector.

(ii) If ${{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}$ is negative, then origin lies in the acute angle between the given planes provided ${{d}_{1}}$ and ${{d}_{2}}$ are of same sign and if ${{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}$ is positive, then origin lies in the obtuse angle between the given planes.

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