Find the image of the point
Question: Find the image of the point $(5,9,3)$ in the line $\frac{x-1}{2}=\frac{y=2}{3}=\frac{z-3}{4}$. Solution:...
Read More →Find the image of the point
Question: Find the image of the point $(0,2,3)$ in the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$. Solution:...
Read More →Find the coordinates of the foot of the perpendicular drawn from the point
Question: Find the coordinates of the foot of the perpendicular drawn from the point $A(1,8,4)$ to the line joining the points $B(0,-1,3)$ and $C(2,-3,-1)$. Solution:...
Read More →Find the coordinates of the foot of the perpendicular drawn from the point
Question: Find the coordinates of the foot of the perpendicular drawn from the point $A(1,2,1)$ to the line joining the points $B(1,4,6)$ and $C(5,4,4)$. Solution:...
Read More →Find the vector equation of a line passing through the point having the position vector
Question: Find the vector equation of a line passing through the point having the position vector $(\hat{i}+2 \hat{j}-3 \hat{k})$ and parallel to the line joining the points with position vectors $(\hat{\mathrm{i}}-\hat{\mathrm{j}}+5 \hat{\mathrm{k}})$ and $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})$. Also, find the Cartesian equivalents of this equation. Solution:...
Read More →Find the vector equation of a line passing through the point
Question: Find the vector equation of a line passing through the point $A(3,-2,1)$ and parallel to the line joining the points $B(-2,4,2)$ and $C(2,3,3)$. Also, find the Cartesian equations of the line. Solution:...
Read More →Find the vector and Cartesian equations of the line joining the points whose position vectors are
Question: Find the vector and Cartesian equations of the line joining the points whose position vectors are $(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ and $(\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ Solution:...
Read More →Find the vector and Cartesian equations of the line passing through the points
Question: Find the vector and Cartesian equations of the line passing through the points $A(2,-3,0)$ and $B(-2,4$, 3). Solution:...
Read More →Find the vector and Cartesian equations of the line passing through the points
Question: Find the vector and Cartesian equations of the line passing through the points $A(3,4,-6)$ and $B(5,-2$, 7). Solution:...
Read More →Find the length and the foot of the perpendicular drawn from the point
Question: Find the length and the foot of the perpendicular drawn from the point $(2,-1,5)$ to the line $\frac{x-11}{10}=\frac{y+2}{-4}=\frac{z+8}{-11}$ Solution:...
Read More →Find the coordinates of the foot of the perpendicular drawn from the point
Question: Find the coordinates of the foot of the perpendicular drawn from the point $(1,2,3)$ to the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Also, find the length of the perpendicular from the given point to the line. Solution:...
Read More →Solve this following
Question: Show that the lines $\frac{x-1}{2}=\frac{y+1}{3}=z$ and $\frac{x+1}{5}=\frac{y-2}{1}, z=2$ do not intersect each other. Solution:...
Read More →Solve this following
Question: Show that the lines $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}-3}{4}$ and $\frac{\mathrm{x}-4}{5}=\frac{\mathrm{y}-1}{2}=\mathrm{z}$ intersect each other. Also, find the point of their intersection. Solution:...
Read More →Prove that the lines
Question: Prove that the lines $\frac{\mathrm{x}-4}{1}=\frac{\mathrm{y}+3}{4}=\frac{\mathrm{z}+1}{7}$ and $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{-3}=\frac{\mathrm{z}+10}{8}$ intersect each other and find the point of their intersection. Solution:...
Read More →Find the Cartesian and vector equations of the line passing through the point
Question: Find the Cartesian and vector equations of the line passing through the point $(1,2,-4)$ and perpendicular to each of the lines $\frac{x-8}{8}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y+29}{8}=\frac{z-5}{-5}$. Solution:...
Read More →Find the equations of the line passing through the point
Question: Find the equations of the line passing through the point $(-1,3,-2)$ and perpendicular to each of the lines $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ and $\frac{x+2}{-3}=\frac{y-1}{2}=\frac{z+1}{5}$. Solution:...
Read More →Find the Cartesian and vector equations of a line which passes through the point
Question: Find the Cartesian and vector equations of a line which passes through the point $(1,2,3)$ and is parallel to the line $\frac{-x-2}{1}=\frac{y+3}{7}=\frac{2 z-6}{3}$. Solution:...
Read More →Find the equations of the line passing through the point
Question: Find the equations of the line passing through the point $(1,-2,3)$ and parallel to the line $\frac{x-6}{3}=\frac{y-2}{-4}=\frac{z+7}{5}$. Also find the vector form of this equation so obtained. Solution:...
Read More →Find the Cartesian equations of the line which passes through the point
Question: Find the Cartesian equations of the line which passes through the point $(1,3,-2)$ and is parallel to the line given by $\frac{\mathrm{x}+1}{3}=\frac{\mathrm{y}-4}{5}=\frac{\mathrm{z}+3}{-6}$. Also, find the vector form of the equations so obtained. Solution:...
Read More →The Cartesian equations of a line are
Question: The Cartesian equations of a line are $3 x+1=6 y-2=1-z$. Find the fixed point through which it passes, its direction ratios and also its vector equation. Solution:...
Read More →The Cartesian equations of a line are
Question: The Cartesian equations of a line are $\frac{x-3}{2}=\frac{y+2}{-5}=\frac{z-6}{4}$. Find the vector equation of the line. Solution:...
Read More →A line is drawn in the direction of
Question: A line is drawn in the direction of $(\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ and it passes through a point with position vector $(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-4 \hat{\mathrm{k}}) .$ Find the equations of the line in the vector as well as Cartesian forms. Solution:...
Read More →Find the vector equation of the line passing through the point with position vector
Question: Find the vector equation of the line passing through the point with position vector $(2 \hat{j}+\hat{j}-5 \hat{k})$ and parallel to the vector $(\hat{i}+3 \hat{j}-\hat{k})$. Deduce the Cartesian equations of the line. Solution:...
Read More →A line passes through the point
Question: A line passes through the point $(2,1,-3)$ and is parallel to the vector $(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$. Find the equations of the line in vector and Cartesian forms. Solution:...
Read More →A line passes through the point
Question: A line passes through the point $(3,4,5)$ and is parallel to the vector $(2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})$. Find the equations of the line in the vector as well as Cartesian forms. Solution:...
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