English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative:The unit vector parallel to the resultant of the vectors ijki^+j^-k^ and ijki^-2j^+k^ is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is

Options

  • `(hat"i" - hat"j" + hat"k")/sqrt(5)`

  • `(2hat"i" + hat"j")/sqrt(5)`

  • `(2hat"i" - hat"j" + hat"k")/sqrt(5)`

  • `(2hat"i" - hat"j")/sqrt(5)`

MCQ

Solution

`(2hat"i" - hat"j")/sqrt(5)`

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Vector Algebra - Exercise 8.5 [Page 80]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 8 Vector Algebra
Exercise 8.5 | Q 3 | Page 80

RELATED QUESTIONS

If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.

(A) `0,1/sqrt2,-1/sqrt2`

(B) `0,-1/sqrt2,-1/sqrt2`

(C) `1,1/sqrt2,1/sqrt2`

(D) `0,-1/sqrt2,1/sqrt2`


Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.


Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.


Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.


Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).


What are the direction cosines of X-axis?


What are the direction cosines of Z-axis?


Write the distance of the point P (xyz) from XOY plane.


Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.


Find the distance of the point (2, 3, 4) from the x-axis.


If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?


A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is


Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.


If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a


The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.


If the directions cosines of a line are k,k,k, then ______.


The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.


A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.


A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×