Please help/verify the answer.
1. When you add vectors geometrically:
a) vectors are aligned tail to tail
b) vectors are aligned head to head
c) vectors are aligned head to tail
d) vectors are put side by side
Is the answer D?
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2. Adding a vector to the zero vector:
a) produces zero vector
b) preserves the non-zero vector
c) changes the vector's direction
d) reduces the vector's magnitude
Answer is B?
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3. If A⃗ is any non-zero vector, a unit vector in the same direction of A⃗ would be:
a) |A⃗|A⃗
b) (1/|A⃗|) A⃗
c) (-1/|A⃗|) A⃗
d) -|A⃗|A⃗
Answer is A?
1c, 2b, 3b
You got one out of three. Were you just guessing?
1. The correct answer is B) vectors are aligned head to head.
When you add vectors geometrically, you align the vectors head to head. This means that the tail of the second vector is placed at the head of the first vector. The resulting vector is then drawn from the tail of the first vector to the head of the second vector.
So, the correct answer is B) vectors are aligned head to head.
2. The correct answer is B) preserves the non-zero vector.
When you add a vector to the zero vector, it does not change the non-zero vector. The zero vector has no magnitude or direction, so adding any vector to it will not change the magnitude or direction of the non-zero vector.
So, the correct answer is B) preserves the non-zero vector.
3. The correct answer is b) (1/|A|)A.
A unit vector is a vector with a magnitude of 1. To find a unit vector in the same direction as vector A, divide vector A by its magnitude |A|.
So, the correct answer is b) (1/|A|)A.
To verify the answers for the given questions:
1. When adding vectors geometrically, the correct choice is c) vectors are aligned head to tail.
When adding vectors geometrically, you align the second vector head to tail with the first vector. This allows you to form a triangle or a polygon where the resultant vector is the diagonal of the polygon formed.
Therefore, the answer is c) vectors are aligned head to tail.
2. When adding a vector to the zero vector, the correct choice is b) preserves the non-zero vector.
The zero vector, denoted as 0⃗, has no magnitude or direction but does not change the non-zero vector being added to it. The non-zero vector, also called the initial vector or original vector, preserves its direction and magnitude when added to the zero vector.
So, the answer is b) preserves the non-zero vector.
3. If A⃗ is any non-zero vector, a unit vector in the same direction as A⃗ would be:
The definition of a unit vector is a vector with a magnitude of 1. To find a unit vector in the same direction as A⃗, we need to divide A⃗ by its magnitude, |A⃗|.
Hence, the correct choice is b) (1/|A⃗|) A⃗.
Therefore, the answer is b) (1/|A⃗|) A⃗.
In conclusion, the correct answers are:
1. c) vectors are aligned head to tail.
2. b) preserves the non-zero vector.
3. b) (1/|A⃗|) A⃗.