Problem: Text: The remainder of the expression is arrived at by finding an arbitrary point on the line. To do so, consider that any point in space may be written as r = c 1 n 1 + c 2 n 2 + ( n 1 n 2 ) (\displaystyle (\mathbf (r))=c_(1)(\mathbf (n))_(1)+c_(2)(\mathbf (n))_(2)+\lambda ((\mathbf (n))_(1) imes (\mathbf (n))_(2))) , since ( n 1 , n 2 , ( n 1 n 2 ) ) (\displaystyle \((\mathbf (n))_(1),(\mathbf (n))_(2),((\mathbf (n))_(1) imes (\mathbf (n))_(2))\)) is a basis. We wish to find a point which is on both planes (i.e. on their intersection), so insert this equation into each of the equations of the planes to get two simultaneous equations which can be solved for c 1 (\displaystyle c_(1)) and c 2 (\displaystyle c_(2)) .

Question: can one point be in two different planes?
A: yes

Problem: Text: Tonnage of goods shipped by barges on the Missouri River has seen a serious decline from the 1960s to the present. In the 1960s, the USACE predicted an increase to 12 million short tons (11 Mt) per year by 2000, but instead the opposite has happened. The amount of goods plunged from 3.3 million short tons (3.0 Mt) in 1977 to just 1.3 million short tons (1.2 Mt) in 2000. One of the largest drops has been in agricultural products, especially wheat. Part of the reason is that irrigated land along the Missouri has only been developed to a fraction of its potential. In 2006, barges on the Missouri hauled only 200,000 short tons (180,000 t) of products which is equal to the amount of daily freight traffic on the Mississippi.

Question: is there barge traffic on the missouri river?
A: yes

Problem: Text: The Twenty-sixth Amendment (Amendment XXVI) to the United States Constitution prohibits the states and the federal government from using age as a reason for denying the right to vote to citizens of the United States who are at least eighteen years old. The drive to lower the voting age from 21 to 18 grew across the country during the 1960s, driven in large part by (1) the military draft that resulted in young men between the ages of 18 and 21 being conscripted into armed forces, primarily the U.S. Army (or voluntarily enlisting, primarily in one of the other branches of the U.S. armed forces, to avoid the draft) to support military combat operations in Vietnam, and (2) the broader student activism movement protesting the Vietnam War. The impetus for drafting an amendment to lower the voting age arose following the Supreme Court's decision in Oregon v. Mitchell, 400 U.S. 112 (1970), which held that Congress may establish a voting age for federal elections, but not for local or state elections.

Question: did the voting age used to be 21?
A:
yes