
For the following exercises, determine whether the statement is true or false. Justify the answer with a proof or a counterexample.
423. For

Determine whether the statement is true or false. Justify the answer with a proof or a counterexample.
Explanation of Solution
Given information:
For vector
From the given information we know that for vector
We consider
Then we can find dot product as follows.
By the definition of scalar multiplication we can figure out the vector
Therefore the dot product
From (1) and (2) we can say that,
Hence the statement “For vector
Want to see more full solutions like this?
Chapter 2 Solutions
Calculus Volume 3
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics (13th Edition)
- 3) Find an equation for the parabola with a vertex at (1, 2) and focus at (1, 4). A) (x - 1)² = 8(y-2) C) (x - 1)² = -8(y - 2) B) (y - 2)² = -12(x − 1) - D) (y - 2)² = 12(x-1)arrow_forward2) Graph the equation. y² = 12x 5 10 -10 -5 5 + 10 xarrow_forward15) Solve the triangles if possible. B = 11°, b = 15.5, a = 40.62arrow_forward
- 10) Find the exact value of the expression. tan−1 [tan (~ 7}]] 8arrow_forward12) The point (-15, -8) is on the terminal side of an angle in standard position. Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle 0.arrow_forwardFind the critical value for a left-tailed test using the F distribution with a 0.025, degrees of freedom in the numerator=12, and degrees of freedom in the denominator = 50. A portion of the table of critical values of the F-distribution is provided. Click the icon to view the partial table of critical values of the F-distribution. What is the critical value? (Round to two decimal places as needed.)arrow_forward
- 6) Find the center, foci, and vertices of the ellipse. = 9 49 1arrow_forward1) Find an equation of the parabola with a focus at (0, 4) and directrix the line y = -4, and state the two points that define the latus rectum. A) x² = 16y; latus rectum: (4, 8) and (-4,8) B) x² = 4y; latus rectum: (2, 4) and (-2, 4) C) x² = 16y; latus rectum: (8, 4) and (-8, 4) D) y² = 4x; latus rectum: (9, 2) and (-9, 2)arrow_forward4) A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places. A) 0.90 ft B) 0.21 ft C) 0.52 ft D) 0.26 ftarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning

