Solve this following
Question: The angle between the lines $\overrightarrow{\mathrm{r}}=(3 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ and $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-5 \hat{\mathrm{k}})+\mu(3 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})$ is A. $\cos ^{-1}\left(\frac{8 \sqrt{3}}{15}\right)$ B. $\cos ^{-1}\left(\frac{6 \sqrt{2}}{5}\right)$ C. $\cos ^{-1}\left(\frac{5 \sqrt{3}}{8}\right)$ D. $\cos ...
Read More →The angle between the lines
Question: The angle between the lines $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{x-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$ is is A. $\cos ^{-1}\left(\frac{3}{4}\right)$ B. $\cos ^{-1}\left(\frac{5}{6}\right)$ C. $\cos ^{-1}\left(\frac{2}{3}\right)$ D. $\frac{\pi}{3}$ Solution:...
Read More →A line passes through the points
Question: A line passes through the points $A(2,-1,4)$ and $B(1,2,-2)$. The equations of the line $A B$ are A. $\frac{x-2}{-1}=\frac{y+1}{2}=\frac{z-4}{-6}$ B. $\frac{x+2}{-1}=\frac{y+1}{2}=\frac{z-4}{6}$ C. $\frac{x-2}{1}=\frac{y+1}{2}=\frac{z-4}{6}$ D. none of these Solution: ....
Read More →Solve this following
Question: If the lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-1}{1}=\frac{z-6}{-5}$ are perpendicular to each other then $\mathrm{k}=$ ? A. $\frac{-5}{7}$ B. $\frac{5}{7}$ C. $\frac{10}{7}$ D. $\frac{-10}{7}$ Solution:...
Read More →The angle between the lines
Question: The angle between the lines $\frac{x-2}{2}=\frac{y-1}{7}=\frac{z+3}{-3}$ and $\frac{x+2}{-1}=\frac{y-4}{2}=\frac{z-5}{4}$ is A. $\frac{\pi}{6}$ B. $\frac{\pi}{3}$ C. $\frac{\pi}{2}$ D. $\cos ^{-1}\left(\frac{3}{8}\right)$ Solution:...
Read More →The direction ratios of two lines are
Question: The direction ratios of two lines are $a, b, c$ and $(b-c),(c-a),(a-b)$ respectively. The angle between these lines is A. $\frac{\pi}{3}$ B. $\frac{\pi}{2}$ C. $\frac{\pi}{4}$ D. $\frac{3 \pi}{4}$ Solution:...
Read More →The direction ratios of two lines are
Question: The direction ratios of two lines are $3,2,-6$ and $1,2,2$, respectively. The acute angle between these lines is A. $\cos ^{-1}\left(\frac{5}{18}\right)$ B. $\cos ^{-1}\left(\frac{3}{20}\right)$ C. $\cos ^{-1}\left(\frac{5}{21}\right)$ D. $\cos ^{-1}\left(\frac{8}{21}\right)$ Solution:...
Read More →What is the angle between the vector
Question: What is the angle between the vector $\overrightarrow{\mathrm{r}}=(4 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ and the $x$-axis? Solution:...
Read More →What are the direction cosines of the vector
Question: What are the direction cosines of the vector $(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ ? Solution:...
Read More →What are the direction cosines of the y-axis?
Question: What are the direction cosines of the $y$-axis? Solution:...
Read More →Solve this following
Question: A line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive directions of $x$-axis, $y$-axis and $z$-axis respectively. what are the direction cosines of the line? Solution:...
Read More →The direction ratios of a line are
Question: The direction ratios of a line are $2,6,-9 .$ What are its direction cosines? Solution:...
Read More →Solve this following
Question: Show that the lines $\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}$ and $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ are at right angles. Solution:...
Read More →Find the angle between the lines
Question: Find the angle between the lines $\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$ and $\frac{x+1}{1}=\frac{y-4}{1}=\frac{z-5}{2}$. Solution:...
Read More →Find the angle between the lines
Question: Find the angle between the lines $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})$ and $\overrightarrow{\mathrm{r}}=(7 \hat{\mathrm{i}}-6 \hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})$. Solution:...
Read More →Find the Cartesian equation of a line which passes through the point having position vector
Question: Find the Cartesian equation of a line which passes through the point having position vector $(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}})$ and is in the direction of the vector $(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})$. Solution:...
Read More →Find the Cartesian equation of a line which passes through the point
Question: Find the Cartesian equation of a line which passes through the point $(-2,4,-5)$ and which is parallel to the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$. Solution:...
Read More →The vector equation of a line is
Question: The vector equation of a line is $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-4 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})$. Find its Cartesian 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 $(1,2,3)$ and parallel to the vector $(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ Solution:...
Read More →The Cartesian equations of a line are
Question: The Cartesian equations of a line are $\frac{x-1}{2}=\frac{y+2}{3}=\frac{5-z}{1}$. Find its vector equation. Solution:...
Read More →The equations of a line are
Question: The equations of a line are $\frac{4-x}{2}=\frac{y+3}{2}=\frac{z+2}{1}$. Find the direction cosines of a line parallel to this line. Solution:...
Read More →Solve this following
Question: If $P(1,5,4)$ and $Q(4,1,-2)$ be two given points, find the direction ratios of $P Q$. Solution:...
Read More →Write the vector equation of a line passing through the point
Question: Write the vector equation of a line passing through the point $(1,-1,2)$ and parallel to the line whose equations are $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$. Solution:...
Read More →The Cartesian equations of a line are
Question: The Cartesian equations of a line are $\frac{3-x}{5}=\frac{y+4}{7}=\frac{2 z-6}{4}$ Write the vector equation of the line. Solution:...
Read More →Write the vector equation of a line whose Cartesian equations are
Question: Write the vector equation of a line whose Cartesian equations are$\frac{x-5}{3}=\frac{y+4}{7}=\frac{6-z}{2}$ Solution:...
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