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If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b?
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If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k ...
Step 1: Define the Vectors
To find the unit vector parallel to vector a + vector b, first define the given vectors:
- Vector a = i + 2j - 3k
- Vector b = y + 4j + 9k
Step 2: Add the Vectors
Now, let's sum the vectors a and b:
- a + b = (1 + y)i + (2 + 4)j + (-3 + 9)k
This simplifies to:
- a + b = (1 + y)i + 6j + 6k
Step 3: Calculate the Magnitude
Next, we need to find the magnitude of the resultant vector:
- Magnitude = sqrt((1 + y)² + 6² + 6²)
This can be calculated as follows:
- Magnitude = sqrt((1 + y)² + 36 + 36)
- Magnitude = sqrt((1 + y)² + 72)
Step 4: Find the Unit Vector
The unit vector parallel to a + b is given by the formula:
- Unit vector = (a + b) / Magnitude
Substituting our values:
- Unit vector = [(1 + y)i + 6j + 6k] / sqrt((1 + y)² + 72)
Step 5: Final Expression
Thus, the unit vector parallel to a + b is:
- Unit vector = (1 + y)/sqrt((1 + y)² + 72) i + 6/sqrt((1 + y)² + 72) j + 6/sqrt((1 + y)² + 72) k
This expression provides the direction of the resultant vector a + b in unit form, which can be further simplified if the specific value of y is known.
To find the unit vector parallel to vector a + vector b, first define the given vectors:
- Vector a = i + 2j - 3k
- Vector b = y + 4j + 9k
Step 2: Add the Vectors
Now, let's sum the vectors a and b:
- a + b = (1 + y)i + (2 + 4)j + (-3 + 9)k
This simplifies to:
- a + b = (1 + y)i + 6j + 6k
Step 3: Calculate the Magnitude
Next, we need to find the magnitude of the resultant vector:
- Magnitude = sqrt((1 + y)² + 6² + 6²)
This can be calculated as follows:
- Magnitude = sqrt((1 + y)² + 36 + 36)
- Magnitude = sqrt((1 + y)² + 72)
Step 4: Find the Unit Vector
The unit vector parallel to a + b is given by the formula:
- Unit vector = (a + b) / Magnitude
Substituting our values:
- Unit vector = [(1 + y)i + 6j + 6k] / sqrt((1 + y)² + 72)
Step 5: Final Expression
Thus, the unit vector parallel to a + b is:
- Unit vector = (1 + y)/sqrt((1 + y)² + 72) i + 6/sqrt((1 + y)² + 72) j + 6/sqrt((1 + y)² + 72) k
This expression provides the direction of the resultant vector a + b in unit form, which can be further simplified if the specific value of y is known.
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If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b?
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If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b?.
If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a vector equals ICAP + 2 J - 3K and b vector equals to Y + 4j + 9k find the unit vector parallel to a + b?.
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