हिंदी

If θ is the angle between two vectors a→ and b→ then, a→⋅b→ ≥ 0, only when - Mathematics

Advertisements
Advertisements

प्रश्न

If θ is the angle between two vectors `veca` and `vecb` then, `veca * vecb` ≥ 0, only when

विकल्प

  • `0 < theta < pi/2`

  • `0 ≤ theta ≤ pi/2`

  • `0 < theta < pi`

  • `0 < theta < pi`

MCQ
Advertisements

उत्तर

`0 ≤ theta ≤ pi/2`

Explanation:

 `veca * vecb  ≥ 0`

⇒ `|veca||vecb| cos theta ≥ 0`

Now, `|veca|` = + ve, = + ve ⇒ `cos theta ≥ 0`

Therefore, `0 ≤ theta ≤ pi/2`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 24: Scalar Or Dot Product - MCQ [पृष्ठ ४९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 24 Scalar Or Dot Product
MCQ | Q 12 | पृष्ठ ४९

वीडियो ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्न

Classify the following as scalars and vector quantities:
(i) Time period
(ii) Distance
(iii) displacement
(iv) Force
(v) Work
(vi) Velocity
(vii) Acceleration


Answer the following as true or false:
\[\vec{a}\] and \[\vec{a}\]  are collinear.


Answer the following as true or false:
Two vectors having same magnitude are collinear.


If \[\vec{a}\] and \[\vec{b}\] are two non-collinear vectors having the same initial point. What are the vectors represented by \[\vec{a}\] + \[\vec{b}\]  and \[\vec{a}\] − \[\vec{b}\].

 


Show that the points (3, 4), (−5, 16) and (5, 1) are collinear.


Using vectors show that the points A (−2, 3, 5), B (7, 0, −1) C (−3, −2, −5) and D (3, 4, 7) are such that AB and CD intersect at the point P (1, 2, 3).


If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-zero, non-coplanar vectors, prove that the following vectors are coplanar:
(1) \[5 \vec{a} + 6 \vec{b} + 7 \vec{c,} 7 \vec{a} - 8 \vec{b} + 9 \vec{c}\text{ and }3 \vec{a} + 20 \vec{b} + 5 \vec{c}\]

(2) \[\vec{a} - 2 \vec{b} + 3 \vec{c} , - 3 \vec{b} + 5 \vec{c}\text{ and }- 2 \vec{a} + 3 \vec{b} - 4 \vec{c}\]

Prove that the following vectors are coplanar:
\[2 \hat{i} - \hat{j} + \hat{k} , \hat{i} - 3 \hat{j} - 5 \hat{k} \text{ and }3 \hat{i} - 4 \hat{j} - 4 \hat{k}\]


Prove that the following vectors are coplanar:
\[\hat{i} + \hat{j} + \hat{k} , 2 \hat{i} + 3 \hat{j} - \hat{k}\text{ and }- \hat{i} - 2 \hat{j} + 2 \hat{k}\]


Prove that the following vectors are non-coplanar:

\[3 \hat{i} + \hat{j} - \hat{k} , 2 \hat{i} - \hat{j} + 7 \hat{k}\text{ and }7 \hat{i} - \hat{j} + 23 \hat{k}\]

If \[\vec{a}\], \[\vec{a}\], \[\vec{c}\] are non-coplanar vectors, prove that the following vectors are non-coplanar: \[2 \vec{a} - \vec{b} + 3 \vec{c} , \vec{a} + \vec{b} - 2 \vec{c}\text{ and }\vec{a} + \vec{b} - 3 \vec{c}\]


If \[\vec{a}\], \[\vec{a}\], \[\vec{c}\] are non-coplanar vectors, prove that the following vectors are non-coplanar: \[\vec{a} + 2 \vec{b} + 3 \vec{c} , 2 \vec{a} + \vec{b} + 3 \vec{c}\text{ and }\vec{a} + \vec{b} + \vec{c}\]


The vectors \[\vec{a} \text{ and } \vec{b}\] satisfy the equations \[2 \vec{a} + \vec{b} = \vec{p} \text{ and } \vec{a} + 2 \vec{b} = \vec{q} , \text{ where } \vec{p} = \hat{i} + \hat{j} \text{ and } \vec{q} = \hat{i} - \hat{j} .\] the angle between \[\vec{a} \text{ and } \vec{b}\] then 


If \[\vec{a} + \vec{b} + \vec{c} = \vec{0} , \left| \vec{a} \right| = 3, \left| \vec{b} \right| = 5, \left| \vec{c} \right| = 7,\] then the angle between \[\vec{a} \text{ and } \vec{b}\] is 


Let \[\vec{a} \text{ and } \vec{b}\]  be two unit vectors and α be the angle between them. Then, \[\vec{a} + \vec{b}\] is a unit vector if 


The vector (cos α cos β) \[\hat{i}\] + (cos α sin β) \[\hat{j}\] + (sin α) \[\hat{k}\]  is a 


If the vectors `hati - 2xhatj + 3 yhatk and hati + 2xhatj - 3yhatk` are perpendicular, then the locus of (x, y) is ______.


What is the length of the longer diagonal of the parallelogram constructed on \[5 \vec{a} + 2 \vec{b} \text{ and } \vec{a} - 3 \vec{b}\] if it is given that \[\left| \vec{a} \right| = 2\sqrt{2}, \left| \vec{b} \right| = 3\] and the angle between \[\vec{a} \text{ and } \vec{b}\] is π/4? 


If \[\vec{a}\] is a non-zero vector of magnitude 'a' and λ is a non-zero scalar, then λ \[\vec{a}\] is a unit vector if 


If \[\vec{a} , \vec{b} , \vec{c}\] are any three mutually perpendicular vectors of equal magnitude a, then \[\left| \vec{a} + \vec{b} + \vec{c} \right|\] is equal to 


The vectors \[2 \hat{i} + 3 \hat{j} - 4 \hat{k}\] and \[a \hat{i} + \hat{b} j + c \hat{k}\] are perpendicular if 


If \[\vec{a} \text{ and } \vec{b}\] are unit vectors inclined at an angle θ, then the value of \[\left| \vec{a} - \vec{b} \right|\] 


If \[\vec{a} \text{ and } \vec{b}\] are two unit vectors inclined at an angle θ, such that \[\left| \vec{a} + \vec{b} \right| < 1,\] then 


Let \[\vec{a} , \vec{b} , \vec{c}\] be three unit vectors, such that \[\left| \vec{a} + \vec{b} + \vec{c} \right|\] =1 and \[\vec{a}\] is perpendicular to \[\vec{b}\]  If \[\vec{c}\] makes angles α and β with \[\vec{a} and \vec{b}\] respectively, then cos α + cos β =


If \[\vec{a} \text{ and }\vec{b}\] be two unit vectors and θ the angle between them, then \[\vec{a} + \vec{b}\] is a unit vector if θ = 


In Figure ABCD is a regular hexagon, which vectors are:
(i) Collinear
(ii) Equal
(iii) Coinitial
(iv) Collinear but not equal.


Which of the following quantities requires both magnitude (size) and direction for its complete description?


In the graphical representation of a vector, what does the arrow length represent?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×