scalar and vector numericals

Dear students scalar and vector numericals pdf of class 11 neet questions and scalar and vector jee questions aiims important questions have been collected at one place to get you all prepared for your neet, aiims ,jee main, advance exams as well as cbse board exams and other board exams. Visit my nawendu classes youtube channel for more help.

1. Magnitudes of two vectors $\vec{a}$ and $\vec{b}$ are 5 unit and 3 unit respectively. If angle between vectors is 60 degree then find (a) $\left| \vec{a}+\vec{b} \right|$

(b) $\left| \vec{a}-\vec{b} \right|$

Answer- (a) 7unit (b) $\sqrt{19}$ unit

2. The component of $9\hat{i}+17\hat{k}$ along Z axis has magnitude

Answer- 17

3. The magnitude of vectors $\overrightarrow{A,}\overrightarrow{B},\overrightarrow{C}$ are 3,4,5 units respectively. If $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ then the angle between $\overrightarrow{A}and\overrightarrow{B}$ is

CBSE PMT 1998

Answer- π/2

4. If two numerically equal forces P and Q acting at a point produces a resultant force of magnitude P then the angle between the two original forces is

AFMC1998

Answer- 120°.

5.Two vectors A and B are such that \[\vec{C}=\vec{A}+\vec{B}and{{\left| {\vec{C}} \right|}^{2}}={{\left| {\vec{A}} \right|}^{2}}+{{\left| {\vec{B}} \right|}^{2}}\] is the angle between positive direction of $\overrightarrow{A}$and $\overrightarrow{B}$then $\theta $ will be l be

AFMC1999

Answer- π/2

6. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

NEET 2016 ,CBSE AIPMT 1991

Answer- ${{90}^{\circ }}$

7. At what angle two forces (P+Q) and (P-Q) act so that resultant is $\sqrt{3{{P}^{2}}+{{Q}^{2}}}$.

Answer- ${{60}^{\circ }}$

8. If vector $\overrightarrow{A}$ and $\overrightarrow{B}$are perpendicular to each other then value of $\alpha $ is

\[\overrightarrow{A}=2\hat{i}+3\hat{j}+8\hat{k}\] ,$\vec{B}=-4\hat{i}+4\hat{j}+\alpha \hat{k}$

CBSE PMT 2005 ,AIIMS 2010

Answer- - ½

9. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces are

CBSE PMT 2003

Answer- Equal to each other in magnitude

10. The angle between two vectors of magnitude 12 and 18 units when their resultant is 24 unit is

CBSE PMT 1999

Answer- 75°52’

11.Find the resultant of three vectors shown in figure.

Answer- $\sqrt{50+10\sqrt{3}}$,${{\tan }^{-1}}\left( \frac{5+\sqrt{3}}{4} \right)$

12. Magnitude and direction of \[\overrightarrow{a}=\hat{i}-\sqrt{3}\hat{j}\]

Answer- 2unit, ${{\tan }^{-1}}\left( -\sqrt{3} \right)$

13. If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ the value of c is

CBSE PMT 1999

Answer- $\sqrt{0.11}$

14.Write unit vector in the direction of \[\overrightarrow{A}=5\hat{i}+\hat{j}-2\hat{k}\]

Answer- $\frac{5}{\sqrt{30}}\hat{i}+\frac{1}{\sqrt{30}}\hat{j}-\frac{2}{\sqrt{30}}\hat{k}$

15. If a particle moves with a velocity given by a vector \[\vec{V}=(6\hat{i}-4\hat{j}+3\hat{k})\] m/s under the influence of a constant force \[\vec{F}=(20\hat{i}+15\hat{j}-5\hat{k})\]N.The instantaneous power applied to the particle is

CBSE PMT 2000

Answer- 45 J/S

16. The $\vec{A}$ and $\vec{B}$ are such that $\left| \vec{A}+\vec{B} \right|=\left| \vec{A}-\vec{B} \right|$ .The angle between the two vectors is

CBSE PMT 2006

Answer- 90°

17. What is the dot products of two vectors of magnitude 3 and 5 if the angle between them is 60 degree.

AFMC 1997

Answer- 7.5 unit

18. Area of parallelogram formed by adjacent sides as the vectors $\vec{A}=3\hat{i}+2\hat{j}$ and $\vec{B}=2\hat{j}-4\hat{k}$ is

Answer= $\sqrt{244}$

19. If \[\left| \vec{A}\times \vec{B} \right|=\frac{\sqrt{3}}{2}AB\] then the value of $\left| \overrightarrow{A}+\overrightarrow{B} \right|$ is

CBSE PMT 2004

Answer- $\sqrt{{{A}^{2}}+{{B}^{2}}+AB}$

20. If the angle between $\vec{A}and\vec{B}$ is $\theta $, the value of the product $\left( \vec{B}X\vec{A} \right).\vec{A}$ is equal to

CBSE PMT 2005

Answer- Zero

21. A body constrained to move in y direction is subjected to force given by \[\vec{F}=(-2\hat{i}+15\hat{j}+6\hat{k})\]N.What is the work done by this force in moving the body through a distance of 10m along y axis

CBSE PMT 1994

Answer- 150 J

22. The result of $\left( \vec{A}X\vec{0} \right)$ will be equal to

CBSE PMT 1992

Answer- Zero vector

23. The angle between two vectors $\vec{A}=3\hat{i}+4\hat{j}+5\hat{k}and\vec{B}=3\hat{i}+4\hat{j}-5\hat{k}$ will be

CBSE PMT 2001

Answer- 90°

24. If $\vec{A}X\vec{B}=\vec{B}X\vec{A}$ ,then angle between $\vec{A}and\vec{B}$ is

AIEEE 2004

Answer- 0

25. A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$.It's speed after 10s is

AIEEE 2009

Answer- $7\sqrt{2}$units

26. The vectors$\vec{p}=a\hat{i}+a\hat{j}+3\hat{k}and\vec{Q}=a\hat{i}+2\hat{j}+\hat{k}$ are perpendicular to each other. The positive value of a is

AFMC 2000

Answer- 3

27. Find component of a vector $\vec{A}=2\hat{i}+3\hat{j}$ along the directions of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$ .

Answer- $\frac{5}{\sqrt{2}}unit,-\frac{1}{\sqrt{2}}unit$

28. Find the torque of a force \[\overrightarrow{F}=-3\hat{i}+ \hat{j}+5\hat{k}\] acting at the point \[\overrightarrow{r}=7\hat{i}+3 \hat{j}+\hat{k}\]

CBSE AIPMT 1997

Answer- $14\hat{i}-38\hat{j}+16\hat{k}$

29.Let \[\overrightarrow{A}=4\hat{i}+3 \hat{j}+2\hat{k}\] and \[\overrightarrow{B}=2\hat{i}-5 \hat{j}+6\hat{k}\] then find

(a) magnitude of $\vec{A}$

(b) magnitude of $\vec{B}$

(d) magnitude of $\vec{A}$-$\vec{B}$

(e) magnitude of 4$\vec{A}$+3$\vec{B}$

(f) magnitude of $\vec{A}$X$\vec{B}$

(g) Vector (or direction) cosines of $\vec{B}$X$\vec{A}$

(h)Unit vector along of ($\vec{A}$-$\vec{B}$)X($\vec{A}$+$\vec{B}$)

(i) Angle between $\vec{A}$ and $\vec{B}$

(j) magnitude of $\vec{A}$.$\vec{B}$

Answer- (a)$\sqrt{29}$unit

(b)$\sqrt{65}$ unit

(d) $\sqrt{84}$ unit

(e) $\sqrt{1169}$ unit

(f) $28\hat{i}-20\hat{j}-26\hat{k}$

(g) $l=-\frac{28}{\sqrt{1860}},m=\frac{20}{\sqrt{1860}},n=\frac{26}{\sqrt{1860}}$

(h) $56\hat{i}-40\hat{j}-52\hat{k}$

(i) ${{\cos }^{-1}}\frac{5}{\sqrt{1885}}or{{\sin }^{-1}}\frac{\sqrt{1860}}{\sqrt{1885}}$

(j) 5 unit

30. Two forces P and Q of magnitude 2F and 3F , respectively are at an angle \[\theta \] with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \[\theta \] is

IIT 2019 Main,10 Jan II

Answer- ${{120}^{\circ }}$

31. Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes . If magnitude of $\vec{A}+\vec{B}$ is equal to n times the magnitude of $\vec{A}-\vec{B}$ , then the angle between $\vec{A}$ and $\vec{B}$ is

IIT 2019 MAIN 10 JAN II, AIIMS 2016

Answer- ${{\cos }^{-1}}\left( \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right)$

32. Let $\left| {{{\vec{A}}}_{1}} \right|=3$, $\left| {{{\vec{A}}}_{2}} \right|=5$ and $\left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|=5$. The value of $\left( 2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}} \right).\left( 3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}} \right)$ is

IIT 2019 MAIN ,08 APRIL II

Answer- -118.5

33. In the cube of of side ‘a’ shown in the figure, the vector form the central point of the face ABOD to the central point of the face BEFO will be

IIT 2019 MAIN 10 JAN I