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Test: Vectors- Case Based Type Questions - JEE MCQ


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20 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Vectors- Case Based Type Questions

Test: Vectors- Case Based Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Vectors- Case Based Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Vectors- Case Based Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vectors- Case Based Type Questions below.
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Test: Vectors- Case Based Type Questions - Question 1

Direction: Read the following text and answer the following questions on the basis of the same:

The cross product of two vectors gives a vector perpendicular to the plane containing the vectors.

Q. If are non-zero vectors, then

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 1

Test: Vectors- Case Based Type Questions - Question 2

Direction: Read the following text and answer the following questions on the basis of the same:

The cross product of two vectors gives a vector perpendicular to the plane containing the vectors.

Q.

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 2

= 1

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Test: Vectors- Case Based Type Questions - Question 3

Direction: Read the following text and answer the following questions on the basis of the same:

The cross product of two vectors gives a vector perpendicular to the plane containing the vectors.

Q.

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 3

Test: Vectors- Case Based Type Questions - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

The cross product of two vectors gives a vector perpendicular to the plane containing the vectors.

Q. The angle between

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 4

The angle between

Test: Vectors- Case Based Type Questions - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

The cross product of two vectors gives a vector perpendicular to the plane containing the vectors.

Q. Area of parallelogram whose adjacent sides are represented by the vectors and sq. units.

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 5

Test: Vectors- Case Based Type Questions - Question 6

Direction: Read the following text and answer the following questions on the basis of the same:

A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let be three non zero vectors.

Q. Let be unit vectors such that and angle between is π/6 then

Test: Vectors- Case Based Type Questions - Question 7

Direction: Read the following text and answer the following questions on the basis of the same:

A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let be three non zero vectors.

Q. then evaluate

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 7

Test: Vectors- Case Based Type Questions - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let be three non zero vectors.

Q. are such that then

Test: Vectors- Case Based Type Questions - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let be three non zero vectors.

Q. are unit vectors and θ be the angle between them then

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 9

Test: Vectors- Case Based Type Questions - Question 10

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 10

Test: Vectors- Case Based Type Questions - Question 11

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1(6, 8, 4), P2(21, 8, 4), P3(21, 16, 10) and P4(6, 16, 10)

Q. What are the components to the vector perpendicular to and the surface of the roof?

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 11

Test: Vectors- Case Based Type Questions - Question 12

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1(6, 8, 4), P2(21, 8, 4), P3(21, 16, 10) and P4(6, 16, 10)

Q. Write the vector in standard notation with and are the unit vectors along the three axes).

Test: Vectors- Case Based Type Questions - Question 13

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1(6, 8, 4), P2(21, 8, 4), P3(21, 16, 10) and P4(6, 16, 10)

Q. What are the components to the two edge vectors defined by = PV of P2 – PV of P1 and = PV of P4 – PV of P1? (where PV stands for position vector)

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 13

∴ A(15, 0,0) and B(0,8,6)

Test: Vectors- Case Based Type Questions - Question 14

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1(6, 8, 4), P2(21, 8, 4), P3(21, 16, 10) and P4(6, 16, 10)

Q. What are the magnitudes of the vectors and in what units?

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 14

Test: Vectors- Case Based Type Questions - Question 15

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1(6, 8, 4), P2(21, 8, 4), P3(21, 16, 10) and P4(6, 16, 10)

Q. What is the magnitude of and in what units?

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 15

Test: Vectors- Case Based Type Questions - Question 16

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. The diagonal

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 16

Test: Vectors- Case Based Type Questions - Question 17

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. The vector

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 17

Test: Vectors- Case Based Type Questions - Question 18

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. Area of ABCD = _______ sq. units.

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 18

Test: Vectors- Case Based Type Questions - Question 19

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. The length of side CD is _______ units.

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 19

Test: Vectors- Case Based Type Questions - Question 20

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. The diagonal

Detailed Solution for Test: Vectors- Case Based Type Questions - Question 20

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