मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

The Measure of Acute Angle Between the Lines Whose Direction Ratios Are 3, 2, 6 and –2, 1, 2 is ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The measure of the acute angle between the lines whose direction ratios are 3, 2, 6 and –2, 1, 2 is ______.

उत्तर

`cos theta = |(3xx-2+2xx1+6xx2)/(sqrt((3)^2+(2)^2+(6)^2)sqrt((-2)^2+1^2 +2^2))|`

=`|(-6+2+12)/(sqrt49sqrt9)| = 8/(7xx3) = 8/21`

`=> theta = cos^(-1) (8/21)`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2017-2018 (March)

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

If the angle between the lines represented by ax2 + 2hxy + by2 = 0 is equal to the angle between the lines 2x2 - 5xy + 3y2 =0,

then show that 100(h2 - ab) = (a + b)2


Find the acute angle between the lines whose direction ratios are 5, 12, -13 and 3, - 4, 5.


Find the angle between the following pair of lines:

`vecr = 2hati - 5hatj + hatk + lambda(3hati - 2hatj + 6hatk) and vecr = 7hati - 6hatk + mu(hati + 2hatj + 2hatk)`


Find the angle between the following pairs of lines: 

`(x-2)/2 = (y-1)/5 = (z+3)/(-3)` and `(x+2)/(-1) = (y-4)/8 = (z -5)/4`


Find the values of p so the line `(1-x)/3 = (7y-14)/2p = (z-3)/2` and `(7-7x)/(3p) = (y -5)/1 = (6-z)/5` are at right angles.


Find the angle between the lines whose direction ratios are a, b, c and b − c, c − a, a − b.


Find the angle between the line \[\vec{r} = \left( 2 \hat{i}+ 3 \hat {j}  + 9 \hat{k}  \right) + \lambda\left( 2 \hat{i} + 3 \hat{j}  + 4 \hat{k}  \right)\]  and the plane  \[\vec{r} \cdot \left( \hat{i}  + \hat{j}  + \hat{k}  \right) = 5 .\]

 

Find the angle between the line \[\frac{x - 1}{1} = \frac{y - 2}{- 1} = \frac{z + 1}{1}\]  and the plane 2x + y − z = 4.

  

The line  \[\vec{r} = \hat{i} + \lambda\left( 2 \hat{i} - m \hat{j}  - 3 \hat{k}  \right)\]  is parallel to the plane  \[\vec{r} \cdot \left( m \hat{i}  + 3 \hat{j}  + \hat{k}  \right) = 4 .\] Find m

 

Find the angle between the line \[\frac{x - 2}{3} = \frac{y + 1}{- 1} = \frac{z - 3}{2}\] and the plane

3x + 4y + z + 5 = 0.

  

State when the line \[\vec{r} = \vec{a} + \lambda \vec{b}\]  is parallel to the plane  \[\vec{r} \cdot \vec{n} = d .\]Show that the line  \[\vec{r} = \hat{i}  + \hat{j}  + \lambda\left( 3 \hat{i}  - \hat{j}  + 2 \hat{k}  \right)\]  is parallel to the plane  \[\vec{r} \cdot \left( 2 \hat{j} + \hat{k} \right) = 3 .\]   Also, find the distance between the line and the plane.

 
 

Show that the plane whose vector equation is \[\vec{r} \cdot \left( \hat{i}  + 2 \hat{j}  - \hat{k}  \right) = 1\] and the line whose vector equation is  \[\vec{r} = \left( - \hat{i}  + \hat{j} + \hat{k}  \right) + \lambda\left( 2 \hat{i}  + \hat{j}  + 4 \hat{k}  \right)\]   are parallel. Also, find the distance between them. 


Write the angle between the line \[\frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z + 3}{- 2}\]  and the plane x + y + 4 = 0. 

 

Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l2 + m2 – n2 = 0.


Show that the straight lines whose direction cosines are given by 2l + 2m – n = 0 and mn + nl + lm = 0 are at right angles.


`vecr = 2hati - 5hatj + hatk + lambda(3hati + 2hatj + 6hatk)` and `vecr = 2hati - 5hatj + hatk + lambda(3hati + 2hatj + 6hatk)`


`vecr = 3hati + hatj + 2hatk + l(hati - hatj + 2hatk)` and `vecr = 2hati + hatj + 56hatk + m(3hati - 5hatj + 4hatk)`


Assertion (A): The acute angle between the line `barr = hati + hatj + 2hatk  + λ(hati - hatj)` and the x-axis is `π/4`

Reason(R): The acute angle 𝜃 between the lines `barr = x_1hati + y_1hatj + z_1hatk  + λ(a_1hati + b_1hatj + c_1hatk)` and  `barr = x_2hati + y_2hatj + z_2hatk  + μ(a_2hati + b_2hatj + c_2hatk)` is given by cosθ = `(|a_1a_2 + b_1b_2 + c_1c_2|)/sqrt(a_1^2 + b_1^2 + c_1^2 sqrt(a_2^2 + b_2^2 + c_2^2)`


The angle between two lines `(x + 1)/2 = (y + 3)/2 = (z - 4)/(-1)` and `(x - 4)/1 = (y + 4)/2 = (z + 1)/2` is ______.


A straight line L through the point (3, –2) is inclined at an angle of 60° to the line `sqrt(3)x + y` = 1. If L also intersects the x-axis, then the equation of L is ______.


The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is ______.


Find the angle between the following two lines:

`vecr = 2hati - 5hatj + hatk + λ(3hati + 2hatj + 6hatk)`

`vecr = 7hati - 6hatk + μ(hati + 2hatj + 2hatk)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×