engineering recuitment AAI ATC Junior Executive 2025 Mock Test Series Mathematics Three Dimensional Geometry Equation of a Plane
Determine the vector equation of the plane passing through the intersection of the planes \(\vec{r} \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=6\) and \(\vec{r}. (2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})=-5\), and the point (1, 1, 1)?
1
\(\vec{r} \cdot(10 \hat{\imath}+13 \hat{\jmath}+23 \hat{k})=69\)
2
\(\vec{r} \cdot(20 \hat{\imath}+23 \hat{\jmath}+26 \hat{k})=69\)
3
\(\vec{r} \cdot(30 \hat{\imath}+23 \hat{\jmath}+13 \hat{k})=69\)
4
\(\vec{r} \cdot(10 \hat{\imath}+23 \hat{\jmath}+13 \hat{k})=69\)