Embibe Experts Solutions for Exercise 3: Assignment

The plane uniquely determined by $x$-axis and $y$-axis is known as

A parallelopiped is formed by planes drawn through the points $\left(1,2,3\right)$ and $\left(6,8,18\right)$ parallel to the coordinate planes then which of the following is not the length of an edge of the rectangular parallelopiped?

The coordinates of the point where the line joining $\left(3,4,1\right)$ and $\left(5,1,6\right)$ crosses the $XY$-plane are

Two vertices of a triangle are $\left(3,4,2\right)$  and $\left(1,3,3\right)$. If the medians of the triangle intersects at $\left(0,3,-1\right)$, then the coordinates of the third vertex of the triangle are

The ratio in which the plane $2x+3y+5z=1$ divides the line segment joining the points $\left(1,0,0\right)$ and $\left(1,3,-5\right)$ is

If the distance between the points $P\left(a,-8,4\right)$ and $Q\left(-3,-5,4\right)$ is $5$, then possible values of $a$ is/are

If $A=\left(2,-3,7\right),B=\left(-1,4,-5\right)$ and $P$ is a point on the line $AB$ such that $AP:BP=3:2$, then $P$ has the coordinates

If the direction ratios of a line are $1+\lambda ,1-\lambda ,2,$ and it makes an angle of $60°$ with the $y$-axis, then $\lambda$ is