In reference to version 224734d7be7ff0c4a8adb3a206356ea122112f33
(Section: 2.1 Vectors)
"Addition and scalar multiplication work in the same way for vectors of length n": Consider this alternative:
"Addition and scalar multiplication work this way for vectors of any length".
"As it is usually clear from context if a letter represents...": The formal tone of "As" used here is correct, but sounds awkward. Consider the more informal "because".
An alternative: "As it is usually clear from context if a letter represents a vector, we do not decorate vectors in this way." -> "It is usually clear from context when a letter represents a vector, so we do not decorate vectors in this way." or alternate: "Because ... we do not ...".
"Geometrically, the sum of two vectors v , w is obtained as follows: place the tail of w at the head of v . Then v + w is the vector whose tail is the tail of v and whose head is the head of w .":
This is correct, but has some ambiguity in English. Colloquially, a head comes first and a tail follows, so referring to the tail of a vector and the head of a vector is fine, but with a complex construction such as the one cited it leads to confusion. Consider saying "start" and "end" instead for a more clear explanation: ""Geometrically, the sum of two vectors v , w is obtained as follows: place the start of w at the end of v . Then v + w is the vector whose start is the start of v and whose end is the end of w ."
"The parallelogram law for vector addition. Click and drag the heads of [Missing] and w ."
"follows: place the tail of v and w at the same point.": should be "tails". Also, see discussion of head/tail above.
Consider removing "to move them" and "to move it" from the examples.
"Scalar Multiplication A scalar multiple of a vector v has the same (or opposite) direction, but a different length. For instance, 2 v is the vector in the direction of v but twice as long, and − 1 2 v is the vector in the opposite direction of v , but half as long. Note that the set of all scalar multiples of a (nonzero) vector v is a line."
Instead of using "as long", consider "the length". This is correct in English, but readers with a non-English first language (SE Asia) have problems with "half as long" because it translates into something like "small as big" and causes confusion.
Suggest:
Scalar Multiplication A scalar multiple of a vector v has the same (or opposite) direction, but a different length. For instance, 2 v is the vector in the direction of v but twice the length, and − 1 2 v is the vector in the opposite direction of v , but half the length. Note that the set of all scalar multiples of a (nonzero) vector v is a line."
The thermometer display in the controls in the examples start in the middle of the control box, should start at the left of the control box (Firefox and Chrome). The "Linear Combinations" example is correct and looks good; also, the coords box does not say "click and drag to move them".
"Linear Combinations of Three Vectors": coords box is missing "click and drag" text.
The system uses two different decorations for links. This imposes a tiny bit of cognitive load on the reader, and could lead to confusion because one form (faint dots) is harder to see and might be missed or misinterpreted as a non-link decoration - at least at first. Consider using one style for all links using the standard underline. Having a colored link distracts from the flow of text, so uncolored is OK in this usage. Distinguishing between links local to the page, and links to other pages or external pages, is not really a useful hint for the reader.
In reference to version 224734d7be7ff0c4a8adb3a206356ea122112f33
(Section: 2.1 Vectors)
"Addition and scalar multiplication work in the same way for vectors of length n": Consider this alternative: "Addition and scalar multiplication work this way for vectors of any length".
"As it is usually clear from context if a letter represents...": The formal tone of "As" used here is correct, but sounds awkward. Consider the more informal "because".
An alternative: "As it is usually clear from context if a letter represents a vector, we do not decorate vectors in this way." -> "It is usually clear from context when a letter represents a vector, so we do not decorate vectors in this way." or alternate: "Because ... we do not ...".
"Geometrically, the sum of two vectors v , w is obtained as follows: place the tail of w at the head of v . Then v + w is the vector whose tail is the tail of v and whose head is the head of w .": This is correct, but has some ambiguity in English. Colloquially, a head comes first and a tail follows, so referring to the tail of a vector and the head of a vector is fine, but with a complex construction such as the one cited it leads to confusion. Consider saying "start" and "end" instead for a more clear explanation: ""Geometrically, the sum of two vectors v , w is obtained as follows: place the start of w at the end of v . Then v + w is the vector whose start is the start of v and whose end is the end of w ."
"The parallelogram law for vector addition. Click and drag the heads of [Missing] and w ."
"follows: place the tail of v and w at the same point.": should be "tails". Also, see discussion of head/tail above.
Consider removing "to move them" and "to move it" from the examples.
"Scalar Multiplication A scalar multiple of a vector v has the same (or opposite) direction, but a different length. For instance, 2 v is the vector in the direction of v but twice as long, and − 1 2 v is the vector in the opposite direction of v , but half as long. Note that the set of all scalar multiples of a (nonzero) vector v is a line." Instead of using "as long", consider "the length". This is correct in English, but readers with a non-English first language (SE Asia) have problems with "half as long" because it translates into something like "small as big" and causes confusion. Suggest: Scalar Multiplication A scalar multiple of a vector v has the same (or opposite) direction, but a different length. For instance, 2 v is the vector in the direction of v but twice the length, and − 1 2 v is the vector in the opposite direction of v , but half the length. Note that the set of all scalar multiples of a (nonzero) vector v is a line."
The thermometer display in the controls in the examples start in the middle of the control box, should start at the left of the control box (Firefox and Chrome). The "Linear Combinations" example is correct and looks good; also, the coords box does not say "click and drag to move them".
"Linear Combinations of Three Vectors": coords box is missing "click and drag" text.
The system uses two different decorations for links. This imposes a tiny bit of cognitive load on the reader, and could lead to confusion because one form (faint dots) is harder to see and might be missed or misinterpreted as a non-link decoration - at least at first. Consider using one style for all links using the standard underline. Having a colored link distracts from the flow of text, so uncolored is OK in this usage. Distinguishing between links local to the page, and links to other pages or external pages, is not really a useful hint for the reader.