Tag: three dimensional geometry
Questions Related to three dimensional geometry
Assertion ($A$): The points with position vectors $\overline{a},\overline{b},\overline{c}$ are collinear if $2\overline{a}-7\overline{b}+5\overline{c}=0$.
Reason ($R$): The points with position vectors $\overline{a},\overline{b},\overline{c}$ are collinear if $l\overline{a}+m\overline{b}+n\overline{c}=\overline{0}$.
The points with position vectors $\vec{a}+\vec{b},\vec{a}-\vec{b}$ and $\vec{a}+\lambda\vec{b}$ are collinear for
If $A$ is $(2, 4, 5),$ and $B$ is $(-7, -2, 8)$, then which of the following is collinear with$A$ and $B$ is
A point $P$ lies on a line whose ends are $A(1,2,3)$ and $B(2,10,1).$ If $z$ component of $P$ is $7,$ then the coordinates of $P$ are
The vectors $\bar {a}=x\hat {i}-2\hat {j}+5\hat {k}$ and $\bar {b}=\hat {i}+y\hat {j}-z\hat {k}$are collinear if
If the points whose position vectors are $2i+j+k, 6i-j+2k$ and $14i-5j+pk$ are collinear, then the value of p is?
Three points whose position vectors are $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ will be collinear if
Assertion ($A$):
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors, no two of which are collinear. If the vector $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+3\vec{c}$ is collinear with $\vec{a}$, then $\vec{a}+2\vec{b}+6\vec{c}$ is equal to.
If $A$ , $B$ and $C$ are three collinear points, where $A= i + 8 j - 5k $, $ B = 6i-2j$ and $C= 9i + 4j - 3 k$, then $B$ divides $AC$ in the ratio of :