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The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector?
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The vector that must be added to the vector i-3j 2k and 3i 6j-7k so th...
Problem: Find the vector that must be added to the vector i-3j+2k and 3i+6j-7k so that the resultant vector is a unit vector along the y-axis.
Solution:
To obtain a unit vector along the y-axis, the x and z components of the resultant vector must be zero. Therefore, we need to find a vector that will cancel out the x and z components of the sum of the two given vectors.
Let the vector we need to find be denoted by v = xi + yj + zk. Then, the sum of the two given vectors and v is:
(i - 3j + 2k) + (3i + 6j - 7k) + (xi + yj + zk) = (x+4)i + (y+3j) + (2-z)k
For this vector to be a unit vector along the y-axis, we need the x and z components to be zero. Therefore, we need to solve the following system of equations:
x + 4 = 0
2 - z = 0
Solving for x and z, we get:
x = -4
z = 2
Therefore, the vector we need to add to obtain a unit vector along the y-axis is:
v = -4i + 3j + 2k
Hence, the correct option is (B) -4i-2j+5k.
Solution:
To obtain a unit vector along the y-axis, the x and z components of the resultant vector must be zero. Therefore, we need to find a vector that will cancel out the x and z components of the sum of the two given vectors.
Let the vector we need to find be denoted by v = xi + yj + zk. Then, the sum of the two given vectors and v is:
(i - 3j + 2k) + (3i + 6j - 7k) + (xi + yj + zk) = (x+4)i + (y+3j) + (2-z)k
For this vector to be a unit vector along the y-axis, we need the x and z components to be zero. Therefore, we need to solve the following system of equations:
x + 4 = 0
2 - z = 0
Solving for x and z, we get:
x = -4
z = 2
Therefore, the vector we need to add to obtain a unit vector along the y-axis is:
v = -4i + 3j + 2k
Hence, the correct option is (B) -4i-2j+5k.
Community Answer
The vector that must be added to the vector i-3j 2k and 3i 6j-7k so th...
-4i-2j+5k is ur answer
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The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector?
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The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector?.
The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The vector that must be added to the vector i-3j 2k and 3i 6j-7k so that the resultant vector is a unit vector along the y-axis is A) 4i 2j 5k B) -4i-2j 5k C) 3i 4j 5k D) null vector?.
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