Question

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

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Solution

Consider space straight a space vector space straight P with rightwards harpoon with barb upwards on top space given space as comma space bold P bold space bold equals bold space straight i with hat on top space plus space straight j with hat on top space straight P subscript straight x bold space straight i with hat on top space plus straight P subscript straight y space space straight j with hat on top space equals straight i with hat on top space plus space straight j with hat on top space On space comparing space the space components space on space both space sides comma space we space get straight P subscript straight x space equals space straight P subscript straight y space equals 1 space open vertical bar straight P with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of straight P subscript straight x squared plus straight P subscript straight y squared end root space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 2 space space space space space space space space space space... space left parenthesis straight i right parenthesis Hence comma space the space magnitude space of space the space vector space straight i with hat on top space plus space straight j with hat on top space is space square root of 2 space space space space Let space straight theta space be space the space angle space made space by space he space vector space straight P with rightwards harpoon with barb upwards on top space comma space with space the space straight x minus axis comma space as space shown space in space the space following space figure. space

therefore space tan space straight theta space equals space open parentheses straight P subscript straight y over straight P subscript straight x close parentheses space rightwards double arrow space space space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 over 1 close parentheses space equals space 45 to the power of straight o space space space space space space space space space space space space space space... space left parenthesis ii right parenthesis Hence comma space vector space straight i with hat on top space plus space straight j with hat on top space makes space an space angle space of space 45 to the power of straight o space with space the space straight x minus axis. Let comma space bold Q bold space bold equals bold space space space straight i with hat on top space minus space straight j with hat on top space straight i. straight e. comma space straight Q subscript straight x bold space space space straight i with hat on top space minus space straight Q subscript straight y straight j with hat on top space equals straight i with hat on top space minus space straight j with hat on top space straight Q subscript straight x space equals space space straight Q subscript straight y space space equals 1 space open vertical bar bold Q close vertical bar space equals space square root of straight Q subscript straight x squared plus straight Q subscript straight y squared end root space equals space square root of 2 space space space space space space space space space space space space space space space space space space space space... space left parenthesis iii right parenthesis thin space Hence comma space the space magnitude space of space the space vector space space space straight i with hat on top space minus space straight j with hat on top space is space square root of 2 space.

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Motion In A Plane

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

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

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

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.