हिंदी

Two vectors having the same magnitude are collinear. - Mathematics

Advertisements
Advertisements

प्रश्न

Two vectors having the same magnitude are collinear.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

It is not necessary for two vectors with the same magnitude to be parallel to the same line.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Vector Algebra - Exercise 10.1 [पृष्ठ ४२८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 10 Vector Algebra
Exercise 10.1 | Q 5. (iii) | पृष्ठ ४२८

संबंधित प्रश्न

If `bara, barb, bar c` are the position vectors of the points A, B, C respectively and ` 2bara + 3barb - 5barc = 0` , then find the ratio in which the point C divides line segment  AB.


Find the position vector of a point which divides the join of points with position vectors `veca-2vecb" and "2veca+vecb`externally in the ratio 2 : 1


Find the value of 'p' for which the vectors `3hati+2hatj+9hatk and hati-2phatj+3hatk` are parallel


Classify the following measures as scalar and vector.

10 kg


In Figure, identify the following vector.

 

Coinitial


Two collinear vectors are always equal in magnitude.


Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1) directed from A to B.


Show that the vector `hati + hatj + hatk` is equally inclined to the axes OX, OY, and OZ.


Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk`, respectively form the vertices of a right angled triangle.


Find the value of x for which `x(hati + hatj + hatk)` is a unit vector.


If θ is the angle between two vectors `veca` and `vecb`, then `veca . vecb >= 0` only when ______.


Find a vector of magnitude 4 units which is parallel to the vector \[\sqrt{3} \hat{i} + \hat{j}\]


Express \[\vec{AB}\]  in terms of unit vectors \[\hat{i}\] and \[\hat{j}\], when the points are A (4, −1), B (1, 3)
Find \[\left| \vec{A} B \right|\] in each case.


Find the angle between the vectors \[\vec{a} \text{ and } \vec{b}\] where \[\vec{a} = \hat{i} - \hat{j} \text{ and } \vec{b} = \hat{j} + \hat{k}\]


Find the angle between the vectors \[\vec{a} \text{ and } \vec{b}\] \[\vec{a} = 3\hat{i} - 2\hat{j} - 6\hat{k} \text{ and } \vec{b} = 4 \hat{i} - \hat{j} + 8 \hat{k}\]


Find the angle between the vectors \[\vec{a} \text{ and } \vec{b}\]  \[\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k} \text{ and } \vec{b} = 4\hat{i} + 4 \hat{j} - 2\hat{k}\]


Find the angle between the vectors \[\vec{a} = 2 \hat{i} - 3 \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} + \hat{j} - 2 \hat{k}\]


Find the angles which the vector \[\vec{a} = \hat{i} -\hat {j} + \sqrt{2} \hat{k}\] makes with the coordinate axes.


The adjacent sides of a parallelogram are represented by the vectors \[\vec{a} = \hat{i} + \hat{j} - \hat{k}\text{ and }\vec{b} = - 2 \hat{i} + \hat{j} + 2 \hat{k} .\]
Find unit vectors parallel to the diagonals of the parallelogram.


\[\text{If }\vec{a} = 3 \hat{i} - \hat{j} - 4 \hat{k} , \vec{b} = - 2 \hat{i} + 4 \hat{j} - 3 \hat{k}\text{ and }\vec{c} = \hat{i} + 2 \hat{j} - \hat{k} ,\text{ find }\left| 3 \vec{a} - 2 \vec{b} + 4 \vec{c} \right| .\]

 


 If  \[\hat{ a  } \text{ and } \hat{b }\] are unit vectors inclined at an angle θ, prove that

 \[\tan\frac{\theta}{2} = \frac{\left| \hat{a} -\hat{b} \right|}{\left| \hat{a} + \hat{b} \right|}\] 


Show that the vector \[\hat{i} + \hat{j} + \hat{k}\] is equally inclined to the coordinate axes. 

 


If \[\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}\]  \[\vec{b} = \hat{i} + \hat{j} - 2 \hat{k}\]  \[\vec{c} = \hat{i} + 3 \hat{j} - \hat{k}\] find λ such that \[\vec{a}\] is perpendicular to \[\lambda \vec{b} + \vec{c}\]  


If \[\vec{\alpha} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} \text{ and } \vec{\beta} = 2 \hat{i} + \hat{j} - 4 \hat{k} ,\] then express \[\vec{\beta}\] in the form of  \[\vec{\beta} = \vec{\beta_1} + \vec{\beta_2} ,\]  where \[\vec{\beta_1}\] is parallel to \[\vec{\alpha} \text{ and } \vec{\beta_2}\]  is perpendicular to \[\vec{\alpha}\]


If \[\vec{a} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k} , \vec{b} = - \hat{i} + 2 \hat{j} + \hat{k} \text{ and } \vec{c} = 3 \hat{i} + \hat{j}\] \[\vec{a} + \lambda \vec{b}\] is perpendicular to \[\vec{c}\] then find the value of λ. 


If \[\vec{a}  \times  \vec{b}  =  \vec{c}  \times  \vec{d}   \text { and }   \vec{a}  \times  \vec{c}  =  \vec{b}  \times  \vec{d}\] , show that \[\vec{a}  -  \vec{d}\] is parallel to \[\vec{b} - \vec{c}\] where \[\vec{a} \neq \vec{d} \text { and } \vec{b} \neq \vec{c}\] .


If `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.


Find the sine of the angle between the vectors `vec"a" = 3hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" - 2hat"j" + 4hat"k"`.


The altitude through vertex C of a triangle ABC, with position vectors of vertices `veca, vecb, vecc` respectively is:


Area of rectangle having vertices A, B, C and D will position vector `(- hati + 1/2hatj + 4hatk), (hati + 1/2hatj + 4hatk) (hati - 1/2hatj + 4hatk)` and `(-hati - 1/2hatj + 4hatk)` is


Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6x − 12 = 3y + 9 = 2z − 2


Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  `hati + 2hatj - hatk` and `-hati + hatj + hatk`  respectively, internally the ratio 2:1.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×