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BASIC-MATHEMATICS USED IN PHYSICS

BASIC MATHEMATICS USED IN PHYSICS TEST - 3

1 / 20

If \underset{P}{\rightarrow}.\underset{Q}{\rightarrow}= PQ, then angle between \underset{P}{\rightarrow} and \underset{Q}{\rightarrow}is :
यदि \underset{P}{\rightarrow}\underset{Q}{\rightarrow} = PQ हो, तो \underset{P}{\rightarrow}\underset{Q}{\rightarrow} के मध्य कोण होगा

2 / 20

The resultant of \underset{A}{\rightarrow} and \underset{B}{\rightarrow} is perpendicular to \underset{A}{\rightarrow}. What is the angle between \underset{A}{\rightarrow} and \underset{B}{\rightarrow} ?
\underset{A}{\rightarrow}\underset{B}{\rightarrow} का परिणामी \underset{A}{\rightarrow} के लम्बवत् है, तो \underset{A}{\rightarrow}\underset{B}{\rightarrow} के मध्य कोण कितना होगा ?

3 / 20

The unit vector parallel to the resultant of the vectors \underset{A}{\rightarrow} = 4\hat{i} + 3\hat{j} + 6\hat{k} and \underset{B}{\rightarrow} = -\hat{i} + 3\hat{j} - 8\hat{k} is :
सदिश \underset{A}{\rightarrow}= 4\hat{i}+3\hat{j}+6\hat{k}तथा \underset{B}{\rightarrow} =\hat{i}+3\hat{j}-8\hat{k} के परिणामी सदिश के समान्तर एकांक सदिश है

4 / 20

If vectors \underset{P}{\rightarrow}\underset{Q}{\rightarrow}and \underset{R}{\rightarrow} have magnitudes 5, 12 and13 units and \underset{P}{\rightarrow} + \underset{Q}{\rightarrow} = \underset{R}{\rightarrow}, the angle between \underset{Q}{\rightarrow} and\underset{R}{\rightarrow}is :

सदिश \underset{P}{\rightarrow}, \underset{Q}{\rightarrow} और \underset{R}{\rightarrow} के परिमाण क्रमश: 5, 12 और 13 इकाई हैं। यदि \underset{P}{\rightarrow} + \underset{Q}{\rightarrow} = \underset{R}{\rightarrow} हो, तो \underset{Q}{\rightarrow}\underset{R}{\rightarrow} के मध्य कोण होगा

5 / 20

The angle between the two vectors \underset{A}{\rightarrow} =3\hat{j}+4\hat{j}+5\hat{k} and \underset{B}{\rightarrow}=3\hat{i}+4\hat{j}-5\hat{k} will be :
सदिश \underset{A}{\rightarrow} =3\hat{j}+4\hat{j}+5\hat{k} तथा \underset{B}{\rightarrow} =3\hat{i}+4\hat{j}-5\hat{k} के मध्य कोण होगा

6 / 20

What is the component of (3\hat{i} + 4\hat{j}) along (\hat{i} +\hat{j}) ?
सदिश ( 3\hat{i}+4\hat{j}) का सदिश (\hat{i}+\hat{j}) के अनुदिश घटक क्या होगा ?

7 / 20

A vector perpendicular to (4\hat{i} - 3\hat{j}) may be :
(4\hat{i} -3\hat{j}) के लम्बवत् सदिश है

8 / 20

A force (3\hat{i} +2\hat{j}) N displaces an object through a distance (2\hat{i} -3\hat{j}) m. The work (W = \underset{F}{\rightarrow}·\underset{S}{\rightarrow} ) done is :
(3\hat{i} + 2\hat{j}) N का एक बल, एक वस्तु को (2\hat{i}-3\hat{j}) m तक विस्थापित करता है। तो किया गया कार्य (W = \underset{F}{\rightarrow}.\underset{S}{\rightarrow}) है

9 / 20

The vector \underset{P}{\rightarrow} = a\hat{i}+a\hat{j}+3\hat{k}r and \underset{Q}{\rightarrow} = a\hat{i}-2\hat{j}-\hat{k} are perpendicular to each other. The positive value of a is :
यदि सदिश \underset{P}{\rightarrow} = a\hat{i}+a\hat{j}+3\hat{k}\underset{Q}{\rightarrow} = a\hat{i}-2\hat{j}-\hat{k} परस्पर लम्बवत् हो, तो a का धनात्मक मान है।

10 / 20

The magnitudes of vectors \underset{A}{\rightarrow} , \underset{B}{\rightarrow}and \underset{C}{\rightarrow} are respectively 12, 5 and 13 units and \underset{A}{\rightarrow} + \underset{B}{\rightarrow} = \underset{C}{\rightarrow} ,then the angle between \underset{A}{\rightarrow} and \underset{B}{\rightarrow} is :
सदिश \underset{A}{\rightarrow}, \underset{B}{\rightarrow} और \underset{C}{\rightarrow}के परिमाण क्रमश: 12, 5 और 13 इकाई है। यदि \underset{A}{\rightarrow}+ \underset{B}{\rightarrow} = \underset{C}{\rightarrow}हो, तो \underset{A}{\rightarrow}\underset{B}{\rightarrow} के मध्य कोण होगा

11 / 20

The angle that the vector \underset{A}{\rightarrow} =2\hat{i}+3\hat{j}  makes with y-axis is :
सदिश \underset{A}{\rightarrow}= 2\hat{i}+3\hat{j}का Y-अक्ष के साथ कोण है

12 / 20

What is the projection of \underset{A}{\rightarrow} on \underset{B}{\rightarrow} ?
सदिश \underset{A}{\rightarrow} का \underset{B}{\rightarrow} पर प्रक्षेप क्या है ?

13 / 20

If \hat{n} = a\hat{i} + b\hat{j}is perpendicular to the vector (\hat{i} + \hat{j}), then the value of a and b may be :
यदि सदिश \hat{n} = a\hat{i} + b\hat{j}, सदिश (\hat{i}+\hat{j}) के लम्बवत् है, तो a व b के मान होगें

14 / 20

The angle between vectors \left ( \hat{i}+ \hat{j}\right ) and e\left (\hat{j} + \hat{k}\right ) is :
सदिश\left ( \hat{i}+ \hat{j}\right ) व सदिश \left (\hat{j} + \hat{k}\right ) के मध्य कोण है

15 / 20

What is the angle between\underset{A}{\rightarrow} and the resultant of (\underset{A}{\rightarrow}+\underset{B}{\rightarrow} ) and (\underset{A}{\rightarrow} - \underset{B}{\rightarrow} ) ?
सदिश (\underset{A}{\rightarrow}+\underset{B}{\rightarrow}) और सदिश (\underset{A}{\rightarrow}-\underset{B}{\rightarrow}) के परिणामी तथा \underset{A}{\rightarrow} के मध्य कोण क्या है ?

16 / 20

The vector \underset{B}{\rightarrow} = 5\hat{i} + 2\hat{j} - S\hat{k} is perpendicular to the vector \underset{A}{\rightarrow}= 3\hat{i}+ \hat{j} + 2\hat{k} if S=
यदि सदिश \underset{B}{\rightarrow} 5\hat{i}+2\hat{j}-S\hat{k}, एक अन्य सदिश A - 3\hat{i} +\hat{j}+ 2\hat{k} के लम्बवत् है, S का मान होगा

17 / 20

If \underset{A}{\rightarrow} + \underset{B}{\rightarrow} r is a unit vector along x-axis and \underset{A}{\rightarrow} = \hat{i}-\hat{j}+\hat{k}, then what is \underset{B}{\rightarrow}?
यदि \underset{A}{\rightarrow} =\hat{i}-\hat{j}+\hat{k} है, (\underset{A}{\rightarrow}+ \underset{B}{\rightarrow} ) x-अक्ष के अनुदिश एकांक सदिश है, तो \underset{B}{\rightarrow} होगा

18 / 20

The vector sum of two forces is perpendicular to their vector difference. In that case, the force :
दो बलों का सदिश योग उनके सदिश अंतर के लम्बवत् है। इस स्थिति में :

19 / 20

Forces 3N, 4N and 12N act at a point in mutually perpendicular directions. The magnitude of the resultant force is :
3N, 4N व 12N के बल, एक बिन्दु पर, परस्पर लम्बवत् दिशाओं में कार्यरत हैं, तो परिणामी बल का परिमाण होगा

20 / 20

Given that A = B. What is the angle between (\underset{A}{\rightarrow}+\underset{A}{\rightarrow}) and (\underset{A}{\rightarrow}-\underset{B}{\rightarrow}) ?
यदि A = B हो, तो (\underset{A}{\rightarrow}+\underset{B}{\rightarrow}) व (\underset{A}{\rightarrow}-\underset{B}{\rightarrow}) के मध्य कोण है

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