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A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.?
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A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find t...
Angle between A and B:
To find the angle between two vectors, we can use the dot product formula:
A · B = |A| |B| cos(theta)
where A · B is the dot product of A and B, |A| and |B| are the magnitudes of A and B respectively, and theta is the angle between the two vectors.
Using the given values, we can calculate the dot product of A and B:
A · B = (2i^ - 2j^ + 4k^) · (i^ + j^)
= 2(1) + (-2)(1) + 0(0)
= 0
Next, we can calculate the magnitudes of A and B:
|A| = sqrt((2)^2 + (-2)^2 + (4)^2) = sqrt(24)
|B| = sqrt((1)^2 + (1)^2) = sqrt(2)
Substituting these values into the dot product formula, we get:
0 = sqrt(24) sqrt(2) cos(theta)
Solving for theta, we get:
cos(theta) = 0
theta = 90 degrees
Therefore, the angle between A and B is 90 degrees.
Projection of the resultant of A and B on x axis:
To find the projection of a vector onto a specific axis, we can use the dot product formula again.
First, we can find the resultant of A and B by adding the two vectors:
A + B = (2i^ - 2j^ + 4k^) + (i^ + j^)
= 3i^ - j^ + 4k^
Next, we can find the projection of this resultant vector onto the x-axis:
proj_x (A + B) = (A + B) · i^
= (3i^ - j^ + 4k^) · i^
= 3
Therefore, the projection of the resultant of A and B onto the x-axis is 3.
To find the angle between two vectors, we can use the dot product formula:
A · B = |A| |B| cos(theta)
where A · B is the dot product of A and B, |A| and |B| are the magnitudes of A and B respectively, and theta is the angle between the two vectors.
Using the given values, we can calculate the dot product of A and B:
A · B = (2i^ - 2j^ + 4k^) · (i^ + j^)
= 2(1) + (-2)(1) + 0(0)
= 0
Next, we can calculate the magnitudes of A and B:
|A| = sqrt((2)^2 + (-2)^2 + (4)^2) = sqrt(24)
|B| = sqrt((1)^2 + (1)^2) = sqrt(2)
Substituting these values into the dot product formula, we get:
0 = sqrt(24) sqrt(2) cos(theta)
Solving for theta, we get:
cos(theta) = 0
theta = 90 degrees
Therefore, the angle between A and B is 90 degrees.
Projection of the resultant of A and B on x axis:
To find the projection of a vector onto a specific axis, we can use the dot product formula again.
First, we can find the resultant of A and B by adding the two vectors:
A + B = (2i^ - 2j^ + 4k^) + (i^ + j^)
= 3i^ - j^ + 4k^
Next, we can find the projection of this resultant vector onto the x-axis:
proj_x (A + B) = (A + B) · i^
= (3i^ - j^ + 4k^) · i^
= 3
Therefore, the projection of the resultant of A and B onto the x-axis is 3.
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A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find t...
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A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.?
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A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.?.
A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A (A vector) = 2i^ - 2j^ + 4k^ and B (B vector) = i^ + j^, then find the angle between A and B and the projection of the resultant of vector A and B on x axis. please answer with solution.?.
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