Given vectors a=(10,-9) and b=(0,-5) Find the magnitude of the resultant vector: T = 3 a + 26

Given (Ã × B) · Ĉ. (a) Prove that for any three vectors Ā, B, and C, AẢ · (B × C) = (Ả × B) · T (b) Calculate (Á × B) · Ć for vector A with magnitude A = 5.00 and angle 6A = 26.0° (measured from the +x -axis toward the +y -axis), vector B with B = 4.00 and OB 63.0°, and vector C' with magnitude 6.00 and in the +z -direction. Vectors A and B are in the xy -plane.

Let vector a = <5,2,4> and vector b = <-4,2,0>. Find vector 2a+3b

Vector A can be expressed in (i,j,k) notation as 5.0i - 4.0j, and vector B as -7.0i + 2.0j. Determine the value of 3A + 2B in terms of magnitude and angle. The angle can be specified either as a value between 0 and 360 degrees counter- clockwise with respect to the positive x-axis, or as a value between 0 and 90 degrees in the appropriate Cartesian quadrant. Paragraph I + v ... 96% 75°F lılı

Two vectors Á and B have precisely equal mag- nitudes. For the magnitude of A + B to be 100 times larger than the magnitude of Á – B, what must be the angle between them?

A sailboat race course consists of four legs, defined by the displacement vectors ABC, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.70 km, B-5.30 km, and C= 4.40 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find (a) the distance of the fourth leg and (b) the angle. 23.0 (a) Number (b) Number Units Units B Finish- K 35.0 X 40.0⁰ Start

Vector A = (8, 4, -5) and Vector B = (-2, 3, 0). Find the angle between these two vectors.

Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 2.00. What should be the length of B⃗ so that the magnitude of their vector sum is 5.00?

Imagine that you take the cross product A x B, where A-22 +79 and B=10€ +99. What is the z-component of the resulting vector?

Three vectors A, B, and C have the following components: Ax=5.00, Ay=7.00; Bx=4.00, By=3.00; Cx=2.00, Cy=5.00. (a) Find the x and y components of A+B +C. (b) Find the magnitude and direction of A+B+C