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Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is?
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Given to vector a vector is equals to ICAP - 6j cap 4 vector and b v...
Magnitude of the Resultant Vector:
To find the magnitude of the resultant vector, we need to add the given vectors a and b, and then calculate the magnitude of the resultant vector.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
To find the resultant vector, we use the formula:
Resultant = a + b
Resultant = (Î - 6ĵ + 4k̂) + (Î - 2ĵ + 3k̂)
Simplifying the equation:
Resultant = 2Î - 8ĵ + 7k̂
Now, let's calculate the magnitude of the resultant vector using the formula:
Magnitude = √(x^2 + y^2 + z^2)
Magnitude = √(2^2 + (-8)^2 + 7^2)
Magnitude = √(4 + 64 + 49)
Magnitude = √117
Magnitude = 10.82
The magnitude of the resultant vector is approximately 10.82.
Value of a Vector dot a Vector multiplied by b Vector:
To find the value of a vector dot a vector multiplied by b vector, we need to calculate the dot product of vector a with itself, and then multiply the result by vector b.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
Dot product of a vector with itself:
a · a = (Î - 6ĵ + 4k̂) · (Î - 6ĵ + 4k̂)
Expanding the equation:
a · a = Î · Î + Î · (-6ĵ) + Î · 4k̂ - 6ĵ · Î + (-6ĵ) · (-6ĵ) + (-6ĵ) · 4k̂ + 4k̂ · Î + 4k̂ · (-6ĵ) + 4k̂ · 4k̂
Simplifying the equation:
a · a = 1 + 0 + 0 - 0 + 36 + 0 + 0 + 0 + 16
a · a = 53
Now, to find the value of a vector dot a vector multiplied by b vector, we multiply the result of the dot product of a vector with itself by vector b:
(a · a) * b = 53 * (Î - 2ĵ + 3k̂)
The unit vector perpendicular to the plane of a vector and b vector:
To find the unit vector perpendicular to the plane of a vector and b vector, we use the cross product of a vector and b vector.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
Cross product of a vector and b vector:
a x b = | Î ĵ k̂ |
| 1 -6 4 |
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To find the magnitude of the resultant vector, we need to add the given vectors a and b, and then calculate the magnitude of the resultant vector.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
To find the resultant vector, we use the formula:
Resultant = a + b
Resultant = (Î - 6ĵ + 4k̂) + (Î - 2ĵ + 3k̂)
Simplifying the equation:
Resultant = 2Î - 8ĵ + 7k̂
Now, let's calculate the magnitude of the resultant vector using the formula:
Magnitude = √(x^2 + y^2 + z^2)
Magnitude = √(2^2 + (-8)^2 + 7^2)
Magnitude = √(4 + 64 + 49)
Magnitude = √117
Magnitude = 10.82
The magnitude of the resultant vector is approximately 10.82.
Value of a Vector dot a Vector multiplied by b Vector:
To find the value of a vector dot a vector multiplied by b vector, we need to calculate the dot product of vector a with itself, and then multiply the result by vector b.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
Dot product of a vector with itself:
a · a = (Î - 6ĵ + 4k̂) · (Î - 6ĵ + 4k̂)
Expanding the equation:
a · a = Î · Î + Î · (-6ĵ) + Î · 4k̂ - 6ĵ · Î + (-6ĵ) · (-6ĵ) + (-6ĵ) · 4k̂ + 4k̂ · Î + 4k̂ · (-6ĵ) + 4k̂ · 4k̂
Simplifying the equation:
a · a = 1 + 0 + 0 - 0 + 36 + 0 + 0 + 0 + 16
a · a = 53
Now, to find the value of a vector dot a vector multiplied by b vector, we multiply the result of the dot product of a vector with itself by vector b:
(a · a) * b = 53 * (Î - 2ĵ + 3k̂)
The unit vector perpendicular to the plane of a vector and b vector:
To find the unit vector perpendicular to the plane of a vector and b vector, we use the cross product of a vector and b vector.
Given:
a = Î - 6ĵ + 4k̂
b = Î - 2ĵ + 3k̂
Cross product of a vector and b vector:
a x b = | Î ĵ k̂ |
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Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is?
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Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is?.
Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is?.
Solutions for Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? in English & in Hindi are available as part of our courses for JEE.
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Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is?, a detailed solution for Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? has been provided alongside types of Given to vector a vector is equals to ICAP - 6j cap 4 vector and b vector is equals to I cap minus 2 j cap 3 k cap 1. The magnitude of their resultant is 2. The value of a vector dot a vector multiplied b vector 3. The unit vector perpendicular to the plane of a vector and b vector is? theory, EduRev gives you an
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