# Three Dimensional Geometry · Mathematics · AP EAPCET

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AP EAPCET 2022 - 4th July Morning Shift
The point of intersection of the lines $$\mathbf{r}=2 \mathbf{b}+t(6 \mathbf{c}-\mathbf{a})$$ and $$\mathbf{r}=\mathbf{a}+s(\mathbf{b}-3 \mathbf{c})$$...
AP EAPCET 2022 - 4th July Morning Shift
If the point $$(a, 8,-2)$$ divides the line segment joining the points $$(1,4,6)$$ and $$(5,2,10)$$ in the ratio $$m: n$$, then $$\frac{2 m}{n}-\frac{... AP EAPCET 2022 - 4th July Morning Shift If$$(a, b, c)$$are the direction ratios of a line joining the points$$(4,3,-5)$$and$$(-2,1,-8)$$, then the point$$P(a, 3 b, 2 c)$$lies on the p... AP EAPCET 2022 - 4th July Morning Shift The$$x$$-intercept of a plane$$\pi$$passing through the point$$(1,1,1)$$is$$\frac{5}{2}$$and the perpendicular distance from the origin to the ... AP EAPCET 2021 - 20th August Morning Shift If the lines,$$\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda}$$and$$\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$$are coplanar, then$$\sin ^{-1}(\s...
AP EAPCET 2021 - 20th August Morning Shift
The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ meets the line $$\frac{x-3}{... AP EAPCET 2021 - 20th August Morning Shift If the vertices of the triangles are (1, 2, 3), (2, 3, 1), (3, 1, 2) and if H, G, S and I respectively denote its orthocentre, centroid, circumcentre ... AP EAPCET 2021 - 20th August Morning Shift A(2, 3, 4), B(4, 5, 7), C(2,$$-$$6, 3) and D(4,$$-$$4, k) are four points. If the line AB is parallel to CD, then k is equal to AP EAPCET 2021 - 20th August Morning Shift If the direction cosines of two lines are$$\left( {{2 \over 3},{2 \over 3},{1 \over 3}} \right)$$and$$\left( {{5 \over {13}},{{12} \over {13}},0} \...
AP EAPCET 2021 - 19th August Evening Shift
$$X$$ intercept of the plane containing the line of intersection of the planes $$x-2 y+z+2=0$$ and $$3 x-y-z+1=0$$ and also passing through $$(1,1,1)... AP EAPCET 2021 - 19th August Evening Shift Let$$L_1$$(resp,$$L_2$$) be the line passing through$$2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$$(resp.$$2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\...
AP EAPCET 2021 - 19th August Evening Shift
If the points (2, 4, $$-$$1), (3, 6, $$-$$1) and (4, 5, $$-$$1) are three consecutive vertices of a parallelogram, then its fourth vertex is
AP EAPCET 2021 - 19th August Evening Shift
$$A(-1,2-3), B(5,0,-6)$$ and $$C(0,4,-1)$$ are the vertices of a $$\triangle A B C$$. The direction cosines of internal bisector of $$\angle B A C$$ a...
AP EAPCET 2021 - 19th August Evening Shift
If the projections of the line segment AB on xy, yz and zx planes are $$\sqrt{15},\sqrt{46},7$$ respectively, then the projection of AB on Y-axis is...
AP EAPCET 2021 - 19th August Evening Shift
Find the equation of the plane passing through the point $$(2,1,3)$$ and perpendicular to the planes $$x-2 y+2 z+3=0$$ and $$3 x-2 y+4 z-4=0$$.
AP EAPCET 2021 - 19th August Morning Shift
The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, $$-$$4) is
AP EAPCET 2021 - 19th August Morning Shift
The direction cosines of a line which makes equal angles with the coordinate axes are
AP EAPCET 2021 - 19th August Morning Shift
Let $$O$$ be the origin and $$P$$ be a point which is at a distance of 3 units from the origin. If the direction ratios of $$\overline{O P}$$ are (1...
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