English

Determine a→×b→, given anda→=2i^+3j^andb→=3i^+5j^. - Physics

Advertisements
Advertisements

Question

Determine `veca xx vecb`, given `veca = 2hati + 3hatj and vecb = 3hati + 5hatj`.

Numerical
Advertisements

Solution

Using determinant for vectors in two dimensions,

`veca xx vecb = |(hati,hatj),(a_x,a_y),(b_x,b_y)| = |(hati,hatj),(2,3),(3,5)|`

`= [(2xx5) - (3xx3)]hatk = (10 - 9)hatk = hatk`

`veca xx vecb` gives `hatk`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Mathematical Methods - Exercises [Page 29]

APPEARS IN

Balbharati Physics [English] Standard 11 Maharashtra State Board
Chapter 2 Mathematical Methods
Exercises | Q 3. (i) | Page 29

RELATED QUESTIONS

`hati  "and"  hatj` are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors `hati+hatj` and `hati-hatj` ? What are the components of a vector `A = 2hati + 3hatj` along the directions of `hati + hatj` and `hati - hatj` ? [You may use graphical method]


Answer the following question.

Show that `vec"a" = (hat"i" - hat"j")/sqrt2` is a unit vector.


Answer the following question.

If `vec"v"_1 = 3hat"i" + 4hat"j" + hat"k" and vec"v"_2 = hat"i" - hat"j" - hat"k"`, determine the magnitude of `vec"v"_1 + vec"v"_2`.


For `vec v_1 = 2 hat i - 3 hat j` and `vec v_2 = -6hat i + 5 hat j`, determine the magnitude and direction of `vec v_1 + vec v_2`.


Find a vector which is parallel to `vec"v" = hat"i" - 2hat"j"` and has a magnitude 10.


Show that vectors `vec a = 2 hat i + 5 hat j - 6 hat k` and `vec b = hat i + 5/2 hat j - 3 hat k` are parallel.


Walking of a person on the road is an example of


Figure shows the orientation of two vectors u and v in the XY plane.

If `u = ahati + bhatj` and `v = phati + qhatj`

which of the following is correct?


The component of a vector r along X-axis will have maximum value if ______.


What is the process of splitting a single vector into two or more vectors along specific directions called?


What is the defining feature of rectangular components of a vector?


A vector \[\vec V\] = 3î + 4ĵ. What is the magnitude of this vector?


Which of the following correctly represents a vector in a 3D coordinate system using unit vectors?


What is the result of dividing a non-zero vector \[\vec V\] by its own magnitude ∣\[\vec V\]∣?


The unit vector parallel to the resultant of the vectors \[\vec A\] = 4\[\hat i\] + 3\[\hat j\] + 6\[\hat k\] and \[\vec B\] = -\[\hat i\] + 3\[\hat j\] - 8\[\hat k\] is ______.


The component of a vector may be ______.


The vector projection of a vector 3\[\hat i\] + 4\[\hat k\] on Y-axis is ______.


A vector is represented by 3\[\hat i\] + \[\hat j\] + 2\[\hat k\]. Its length in XY plane is ______.


A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×