JEE MAINS PRACTICE · Mathematics
Three Dimensional Geometry
1,052 practice questions for JEE Mains Practice — 449 easy · 431 medium · 172 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
The image of the point with position vector $i+3 \mathbf{k}$ in the plane $r \cdot(i+j+k)=1$ is
MCQ
The image of the point with position vector $\hat{\mathbf{i}}+3 \hat{\mathbf{k}}$ in the plane $\mathbf{r} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=1$ is
MCQ
The distance of the point $(3,8,2)$ from the line $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$ measured parallel to the plane $3 x+2 y-2 z+15=0$, is
MCQ
The reflection of the point $(2,-1,3)$ in the plane $3 x-2 y-z=9$ is
MCQ
If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are the position vectors of $A, B, C$ respectively such that $3 \mathbf{a}+4 \mathbf{b}-7 \mathbf{c}=\mathbf{0}$, then $C$ divides $A B$ in the ratio
MCQ
If a line makes $\alpha, \beta, \gamma$ with the positive direction of $x, y$ and $z$-axes respectively. Then, $\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma$ is equal to
MCQ
If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{\boldsymbol{x}-3}{1}=\frac{\boldsymbol{y}-\boldsymbol{k}}{2}=\frac{z}{1}$ intersect, then $k$ is equal to
MCQ
If $\left(\frac{1}{2}, \frac{1}{3}, n\right)$ are the direction cosines of a line, then the value of $n$ is
MCQ
The image of the point $P(1,3,4)$ in the plane $2 x-y+z+3=0$, is
MCQ
The equation of plane passing through a point $A$ $(2,-1,3)$ and parallel to the vectors $\mathbf{a}=(3,0,-1)$ and $\mathbf{b}=(-3,2,2)$ is
MCQ
The direction cosines of any normal to the $x y$-plane are
MCQ
The vector equation of the plane through the point $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and perpendicular to the line of intersection of the plane $\mathbf{r} \cdot(3…