The two vectors a→ and b→ in the figure have equal magnitudes of 10.2 m and the angles are θ1 = 30° and θ2 = 101°. Find (a) the x component and (b) the y component of their vector sum r→, (c) the magnitude of r→, and (d) the angle r→ makes with the positive direction of the x axis.

Vector A⃗A→ has components AxAx = 5 mm and AyAy = -3 mm. Vector B⃗B→ has a magnitude of 8 mm and makes an angle of 30∘∘ with respect to the positive +xx axis. Find the magnitude of the vector C⃗C→ = 2A⃗A→ + B⃗B→.

Vector a lies in the yz plane 68.0° from the positive direction of the y axis, has a positive z component, and has magnitude 3.70 m. Vector b lies in the xz plane 39.0° from the positive direction of the x axis, has a positive z component, and has magnitude 2.10 m. Find (a) à · 7, (b) the x-component of a × 7, (c) the y-component of a x7, (d) the z-component of a xb, and (e) the angle between a and b.

Vector A→, which is directed along an x axis, is to be added to vector B→, which has a magnitude of 9.30 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 5.10 times that of A→. What is the magnitude of A→?

The three vectors in the figure have magnitudes a = 3.20 m, b = 3.20 m, and c = 10.2 m and angle e = 43.0°. What are (a) the x component and (b) the y component of á ; (c) the x component and (d) the y component of b; and (e) the x component and (f) the y component of ? If 7 = pd + qb, what are the values of (g) p and (h) q? (a) Number Units (b) Number Units (c) Number |Units (d) Number Units (e) Number Units (f) Number |Units (g) Number Units (h) Number Units

A sailboat race course consists of four legs, defined by the displacement vectors A, B, C, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.90 km, B = 4.90 km, and C= 5.30 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 (. (a) Number i 6.67 (b) Number 21.29 Units Units 0 0 23.0 7 B km + Finish- B 35.0 X 40.0° Start

Two position vectors each start at the origin. The first has a magnitude of 40.5 cm, and is at an angle of 15.0° as measured counterclockwise from the +x-axis. The second has a magnitude of 23.0 cm and an angle of 68.0°, also counterclockwise from the +x-axis. (a) What is the area of the parallelogram (in cm2) that has the two vectors as two of its sides? cm2 (b) What is the length of the longer diagonal of this parallelogram (in cm)? cm

If the vector B⃗B→ has a magnitude of 45 mm and makes an angle of 30 ∘∘ with the +x+x axis, the vector -B⃗B→   has the same direction as B⃗B→ but a magnitude of -45 mm. makes an angle of -30 ∘∘ with the +x+x axis. has a magnitude of 45 mm. has the opposite direction of B⃗B→ and a magnitude of -45 mm.

The two vectors a and b in the figure have equal magnitudes of 13.3 m and the angles are 0₁ = 25º and 0₂ = 104°. Find (a) the x component and (b) the y component of their vector sum, (c) the magnitude of 7, and (d) the angle makes with the positive direction of the x axis. (a) Number (b) Number (c) Number (d) Number IN 8.8 18.5 20.5 65.7 Units Units Units 0₂ 3 3 m Units °(degrees) x

The following vectors are defined (e, ey, ē,) are unit vectors of an orthogonal coordinate system): d = 2ẻ, + ẻ, - 3ể,z b = ëz – 6ẽ, – ẻ, c = 2e, + 3ẻ, + 4ẻ, Determine the following: (1) Scalar product of vectors à and b; (2) Scalar product of vectors b and b; (3) Magnitude of vector b ; (4) Cross product of ä and ä ; (5) Cross product of a and b.