vectors BARNES Flashcards
top number in vectors means
left/ right
positive = right
The vector (3, -5) written using base vectors is
3i - 5j
i is in what direction
the x direction
j is in what direction
the y direction
To add or subtract vectors
add each component separately
To multiply by scalars
multiply each component by that scalar
Parallel vector are
scalar multiples of each other, ie: b = ka if k is negative, the direction is reversed
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If a = i + 2j, b = -3i + pj, c = -2i + 5j
Find the value of p such that b is parallel to a
Find the value of scalar k such that a + kc is parallel to 10i + 23j
p = -6
k = 1/32
If v = (x,y) the magnitude is
IvI = l (x,y) l = square root of x^2 + y^2
unit vector is
a vector with the magnitude of 1
Unit vector in the same direction as a is
a^ = a / lal
Find the angle vector
a) a = 5i + 3j makes with the i direction
b) b = 4i - 7j makes with the i direction
32 degrees
29.7 degrees
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Position vector of point A is
the vector from origin O to point A
It’s written —>OA or a
The displacement vector from point A to point B
—> AB
its calculated as AO + OB
Midpoint M of line segment AB is
½(a + b),
where a and b are the position vectors of A and B
Shape ABCD is a parallelogram if
AD = DC (implying that AD = BC so 2 pairs of parallel sides)
Shape ABCD is a rhombus if in addition
magnitude of AB = magnitude of DC
Points A, B, and C are collinear if
they lie on a straight line
To prove: show AB is // to BC, then state B is a common point
BC = k AB
The vertices of a quadrilateral PQRS have coordinates P(-2, 1), Q(5, -3),
R(6, 0) and S(-1, 5).
The midpoints of sides PQ, QR, RS and SP are A, B, C and D.
Prove that ABCD is a parallelogram.
AB = DC = (4, -0.5)
Three points are A(-3, 2), B(6, 5) and C(12, 7)
Show that A, B and C lie on a straight line
AB = 3/2 BC
Determine whether the points A(4, 2a), B(1, 2a+1) and C(7, 2a-1) are collinear
AB = -2 BC
