1
JEE Advanced 2023 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Let the position vectors of the points $P, Q, R$ and $S$ be $\vec{a}=\hat{i}+2 \hat{j}-5 \hat{k}, \vec{b}=3 \hat{i}+6 \hat{j}+3 \hat{k}$, $\vec{c}=\frac{17}{5} \hat{i}+\frac{16}{5} \hat{j}+7 \hat{k}$ and $\vec{d}=2 \hat{i}+\hat{j}+\hat{k}$, respectively. Then which of the following statements is true?
2
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $H$, let $d(H)$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $H_0$ be a plane in $X$ for which $d\left(H_0\right)$ is the maximum value of $d(H)$ as $H$ varies over all planes in $X$.
Match each entry in List-I to the correct entries in List-II.
The correct option is:
Match each entry in List-I to the correct entries in List-II.
List - I | List - II |
---|---|
(P) The value of $d\left(H_0\right)$ is | (1) $\sqrt{3}$ |
(Q) The distance of the point $(0,1,2)$ from $H_0$ is | (2) $\frac{1}{\sqrt{3}}$ |
(R) The distance of origin from $H_0$ is | (3) 0 |
(S) The distance of origin from the point of intersection of planes $y=z, x=1$ and $H_0$ is | (4) $\sqrt{2}$ |
(5) $\frac{1}{\sqrt{2}}$ |
The correct option is:
3
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let O be the origin and let PQR be an arbitrary triangle. The point S is such that
$$\overrightarrow{OP}$$ . $$\overrightarrow{OQ}$$ + $$\overrightarrow{OR}$$ . $$\overrightarrow{OS}$$ = $$\overrightarrow{OR}$$ . $$\overrightarrow{OP}$$ + $$\overrightarrow{OQ}$$ . $$\overrightarrow{OS}$$ = $$\overrightarrow{OQ}$$ . $$\overrightarrow{OR}$$ + $$\overrightarrow{OP}$$ . $$\overrightarrow{OS}$$
Then the triangle PQR has S as its
$$\overrightarrow{OP}$$ . $$\overrightarrow{OQ}$$ + $$\overrightarrow{OR}$$ . $$\overrightarrow{OS}$$ = $$\overrightarrow{OR}$$ . $$\overrightarrow{OP}$$ + $$\overrightarrow{OQ}$$ . $$\overrightarrow{OS}$$ = $$\overrightarrow{OQ}$$ . $$\overrightarrow{OR}$$ + $$\overrightarrow{OP}$$ . $$\overrightarrow{OS}$$
Then the triangle PQR has S as its
4
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $$-$$ 2z = 5 and 3x $$-$$ 6y $$-$$ 2z = 7 is
Questions Asked from Vector Algebra and 3D Geometry (MCQ (Single Correct Answer))
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