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MATH / A line passes through the distinct vectors a and b. Which of the following are valid parameterizations of the line? (A) a+t(a−b) (B) (3)/(4)a+t⋅(b)/(4) (C) (a+b)/(2)+t⋅(b−a)/(2) (D…

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problem

A line passes through the distinct vectors a\mathbf{a} and b.\mathbf{b}. Which of the following are valid parameterizations of the line? (A) a+t(a−b)\mathbf{a} + t (\mathbf{a} - \mathbf{b}) (B) 34a+t⋅b4\frac{3}{4} \mathbf{a} + t \cdot \frac{\mathbf{b}}{4} (C) a+b2+t⋅b−a2\frac{\mathbf{a} + \mathbf{b}}{2} + t \cdot \frac{\mathbf{b} - \mathbf{a}}{2} (D) a+2b+t(2b−3a)\mathbf{a} + 2 \mathbf{b} + t (2 \mathbf{b} - 3 \mathbf{a}) (E) −b+t(a+b)-\mathbf{b} + t (\mathbf{a} + \mathbf{b}) (F) b+t3(2a−2b)\mathbf{b} + \frac{t}{3} (2 \mathbf{a} - 2 \mathbf{b}) Enter the letters of the correct options, separated by commas.
Plain-text mathematical notation (without MathML)
A line passes through the distinct vectors a and b.  Which of the following are valid parameterizations of the line?

(A) a+t(a−b)

(B) (3)/(4)a+t⋅(b)/(4)

(C) (a+b)/(2)+t⋅(b−a)/(2)

(D) a+2b+t(2b−3a)

(E) −b+t(a+b)

(F) b+(t)/(3)(2a−2b)

Enter the letters of the correct options, separated by commas.
Original LaTeX notation
A line passes through the distinct vectors $\mathbf{a}$ and $\mathbf{b}.$  Which of the following are valid parameterizations of the line?

(A) $\mathbf{a} + t (\mathbf{a} - \mathbf{b})$

(B) $\frac{3}{4} \mathbf{a} + t \cdot \frac{\mathbf{b}}{4}$

(C) $\frac{\mathbf{a} + \mathbf{b}}{2} + t \cdot \frac{\mathbf{b} - \mathbf{a}}{2}$

(D) $\mathbf{a} + 2 \mathbf{b} + t (2 \mathbf{b} - 3 \mathbf{a})$

(E) $-\mathbf{b} + t (\mathbf{a} + \mathbf{b})$

(F) $\mathbf{b} + \frac{t}{3} (2 \mathbf{a} - 2 \mathbf{b})$

Enter the letters of the correct options, separated by commas.

level

Level 4

type

Precalculus

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Source and history

task_id
060ea21e-708c-5f14-aed7-7e7cc8aa24d9
task_key
precalculus--test--060ea21e-708c-5f14-aed7-7e7cc8aa24d9
task_revision_id
1
config / split
precalculus / test

Official source

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