हिंदी

Choose correct alternatives : The vector equation of line 2x – 1 = 3y + 2 = z – 2 is ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose correct alternatives :

The vector equation of line 2x – 1 = 3y + 2 = z – 2 is ______.

विकल्प

  • `barr = (1/2hati - 2/3hatj + 2hatk) + lambda(3hati + 2hatj + 6hatk)`

  • `barr = hati - hatj + (2hati + hatj + hatk)`

  • `barr = (1/2hati - hatj) + lambda(hati - 2hatj + 6hatk)`

  • `barr = (hati + hatj) + lambda(hati - 2hatj + 6hatk)`

MCQ
रिक्त स्थान भरें

उत्तर

The vector equation of line 2x – 1 = 3y + 2 = z – 2 is `bb(underline(barr = (1/2hati - 2/3hatj + 2hatk) + lambda(3hati + 2hatj + 6hatk))`

shaalaa.com
Vector and Cartesian Equations of a Line
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Line and Plane - Miscellaneous Exercise 6 B [पृष्ठ २२३]

संबंधित प्रश्न

Find the vector equation of the line passing through points having position vector `3hati + 4hatj - 7hatk and 6hati - hatj + hatk`.


Find the vector equation of the line passing through the point having position vector `-hat"i" - hat"j" + 2hat"k"  "and parallel to the line" bar"r" = (hat"i" + 2hat"j" + 3hat"k") + λ(3hat"i" + 2hat"j" + hat"k").`


Find the cartesian equations of the line passing through A(–1, 2, 1) and having direction ratios 2, 3, 1.


A(– 2, 3, 4), B(1, 1, 2) and C(4, –1, 0) are three points. Find the Cartesian equations of the line AB and show that points A, B, C are collinear.


A line passes through (3, –1, 2) and is perpendicular to lines `bar"r" = (hat"i" + hat"j" - hat"k") + lambda(2hat"i" - 2hat"j" + hat"k") and bar"r" = (2hat"i" + hat"j" - 3hat"k") + mu(hat"i" - 2hat"j" + 2hat"k")`. Find its equation.


Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.


The foot of the perpendicular drawn from the origin to a plane is M(1,0,0). Find the vector equation of the plane.


Find the vector equation of the line which passes through the point (3, 2, 1) and is parallel to the vector `2hat"i" + 2hat"j" - 3hat"k"`.


Find the Cartesian equations of the line which passes through points (3, –2, –5) and (3, –2, 6).


Find the Cartesian equations of the line passing through the point A(1, 1, 2) and perpendicular to the vectors `barb = hati + 2hatj + hatk and barc = 3hati + 2hatj - hatk`.


Find the Cartesian equations of the line which passes through the point (2, 1, 3) and perpendicular to the lines `(x - 1)/(1) = (y - 2)/(2) = (z - 3)/(3) and x/(-3) = y/(2) = z/(5)`.


Find the vector and Cartesian equations of the line passing through the point (–1, –1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z − 2.


Find the Cartesian equation of the line passing through the origin which is perpendicular to x – 1 = y – 2 = z – 1 and intersect the line `(x - 1)/(2) = (y + 1)/(3) = (z - 1)/(4)`.


Solve the following :

Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector `2hat"i" + hat"j" + 2hat"k"`.


Solve the following :

Find the cartesian equation of the plane passing through A(1,-2, 3) and direction ratios of whose normal are 0, 2, 0.


Solve the following :

Find the cartesian equation of the plane passing through A(7, 8, 6) and parallel to the plane `bar"r".(6hat"i" + 8hat"j" + 7hat"k")` = 0.


Solve the following :

Show that the lines x = y, z = 0 and x + y = 0, z = 0 intersect each other. Find the vector equation of the plane determined by them.


Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).


Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.


Verify if the point having position vector `4hat"i" - 11hat"j" + 2hat"k"` lies on the line `bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + lambda (2hat"i" + 7hat"j" + 3hat"k")`


Find the Cartesian equation of the line passing through  A(1, 2, 3) and having direction ratios 2, 3, 7


Find the direction ratios of the line perpendicular to the lines

`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`


Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)


Find the Cartesian equation of the line passing through (−1, −1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z – 2


Find the Cartesian equation of the plane passing through A(7, 8, 6)and parallel to XY plane


Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)


Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles


Find the Cartesian and vector equation of the plane which makes intercepts 1, 1, 1 on the coordinate axes


The cartesian coordinates of the point on the parabola y2 = x whose parameter is ____________.


The cartesian equation of the line `overliner = (hati + hatj + hatk) + lambda(hatj + hatk)` is ______


If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ is ______.


Equation of Z-axis is ______


The equation of line is `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1`. The co-ordinates of the point on the line at a distance of 3 units from the point (1, -1, -1) is ______ 


The centres of the circles x2 + y2 = 1, x2 + y2 + 6x – 2y = 1 and x2 + y2 – 12x + 4y = 1 are ______.


Find the Cartesian equation of the plane passing through A(–1, 2, 3), the direction ratios of whose normal are 0, 2, 5.


If the line `(x - 1)/2 = (y + 1)/3 = z/4` lies in the plane 4x + 4y – kz = 0, then the value of k is ______.


Find the direction cosines of the line `(2x - 1)/3 = 3y = (4z + 3)/2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×