1
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0 Three lines are given by

$$r = \lambda \widehat i,\,\lambda \in R$$,

$$r = \mu (\widehat i + \widehat j),\,\mu \in R$$ and

$$r = v(\widehat i + \widehat j + \widehat k),\,v\, \in R$$

Let the lines cut the plane x + y + z = 1 at the points A, B and C respectively. If the area of the triangle ABC is $$\Delta$$ then the value of (6$$\Delta$$)2 equals ..............
2
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the Z-axis. Let the distance of P from the X-axis be 5. If R is the image of P in the XY-plane, then the length of PR is ...............
3
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
Let a and b be two unit vectors such that a . b = 0. For some x, y$$\in$$R, let $$\overrightarrow c = x\overrightarrow a + y\overrightarrow b + \overrightarrow a \times \overrightarrow b$$. If | $$\overrightarrow c$$| = 2 and the vector c is inclined at the same angle $$\alpha$$ to both a and b, then the value of $$8{\cos ^2}\alpha$$ is ..............
4
JEE Advanced 2015 Paper 2 Offline
Numerical
+4
-0
Suppose that $$\overrightarrow p ,\overrightarrow q$$ and $$\overrightarrow r$$ are three non-coplanar vectors in $${R^3}$$. Let the components of a vector $$\overrightarrow s$$ along $$\overrightarrow p ,$$ $$\overrightarrow q$$ and $$\overrightarrow r$$ be $$4, 3$$ and $$5,$$ respectively. If the components of this vector $$\overrightarrow s$$ along $$\left( { - \overrightarrow p + \overrightarrow q + \overrightarrow r } \right),\left( {\overrightarrow p - \overrightarrow q + \overrightarrow r } \right)$$ and $$\left( { - \overrightarrow p - \overrightarrow q + \overrightarrow r } \right)$$ are $$x, y$$ and $$z,$$ respectively, then the value of $$2x+y+z$$ is
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