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# Understanding Vectors (Grades 11-12)

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## Understanding Vectors

1.
Another name for the initial point of a vector is called the                 .
1. tail
2. tip
3. direction
4. all of the above
2.
The vectors $4vec(n)$ and $6vec(n)$
1. have nothing in common.
2. have the same direction.
3. have the same start point.
4. have the same magnitude.
3.
The vectors $4vec(n)$ and $-4vec(n)$
1. have nothing in common.
2. have the opposite direction.
3. have the same direction.
4. have the opposite magnitude.
4.
Two vectors with the same direction are equal.
1. They are always equal.
2. They are never equal.
3. It depends on their magnitude.
4. It depends on their end point.
5.
Two vectors with the same magnitude are equal.
1. They are always equal.
2. They are never equal.
3. It depends on their direction.
4. It depends on their initial point.
6.
What is the component form of the vector $vec(JK) ?$
1. $<<-4,4>>$
2. $[[-4],[4]]$
3. $4hat(i) - 4hat(j)$
4. $<<4,-4>>$
7.
These two vectors are parallel.
$<<1/2, 4>>,$ $<<2, 8>>$
1. True
2. False
8.
What is the magnitude of a vector with points $(-2,5)$ and $(4,13) ?$
1. $10$
2. $5$
3. $sqrt(7)$
4. $sqrt(14)$
9.
Let $vec(n) = <<-6,-1>>, vec(m) = <<10,-10>>.$ Find $2vec(m) - 5vec(n)$.
1. $<<10, 25>>$
2. $<<-10, -25>>$
3. $<<50, -15>>$
4. $<<16, 9>>$
10.
Let $vec(a) = 3hat(i) - 6hat(j), vec(b) = -hat(i) + 3hat(j).$ Find $3vec(a) + 2vec(b).$
1. $7hat(i) - 3hat(j)$
2. $2hat(i) - 3hat(j)$
3. $11hat(i) + 24hat(j)$
4. $7hat(i) - 12hat(j)$
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