Which of the following are correct (meaningful) vector expressions? (a) A ( B . C ) (b) Ả ×(B . 7) (c) Á -( B × Ć ) (d) Ã ×(B × ) (e) Á +( B . C) (f) Á +( B × Ć) (g) 5 + A (h) 5+( B . Č ) (1) 5 + ( B × C) (G) ( A B)+( B x C)

Vector A = 7.2 i + 2.6 j. Vector B = 7.5 i + 7.4 j. The magnitude of the cross product i.e. |AxB| is: :

The figure shows two displacement vectors A and B. Vector A points at an angle of 22.0° above the x axis and has an unknown magnitude. Vector B has an x component Bx = 32.0 m and has an unknown y component By. These two vectors are equal. Find (a) the magnitude of A and (b) the value of By. B, 22.0° (a) 0 B₂ 32.0 m (b) (a) Number i (b) Number i Ā +X +X Units Units

Three displacement vectors of a croquet ball are shown in the figure, where |A| 45.0° 45.0° R= Č (a) Find the resultant in unit-vector notation. units (b) Find the magnitude and direction of the resultant displacement. magnitude unit(s) direction o counterclockwise from the +x axis = 19.0 units, |B| = 25.0 units, and |C| = 10.0 units. M

In the cross (or vector) product F = qu x B we know that q = 1 F = −29î + −16ĵ + −18k 6.01 +3.07 + 7.0k V = B = B + BJ + Bi What then is B in unit-vector notation if Bx = By? B = i î+ i Ĵ+ i

Which of the following are correct (meaningful) vector expressions? (a) Ả ·(B. Č) (b) Ả ×(B. 7) (c) Ā :(B x Č) X ( (d) Á ×(B xC) (e) 지 +(B.C) (f) Á +( B × C ) (g) 5 + Á (h) 5+( B. 7 ) В (i) 5 + ( B x Ć ) 6) ( Ả B)+( B x )

Consider a vector a = N i=1 ₁a¡ê; expressed in an orthonormal basis. Which of the following statements are true? Negative marking applies. Select one or more: a. (aa) = ₁ ai N i=1 b. (ala) (a|a) = 0 N (a|a) = Σ;₁a;ªz •j=1 □ d. e. f. = (ala) = (aa) = g. (aa) = 1 N ₁a²/ N i=1 * ₁ ažai ₁|a₁|² N

Vector C can be written (-3i+1j) cm O (-4i+2j) cm O (i-3j) cm (2i+-4j) cm 1 y (cm) 2 1 x (cm)

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 = 3.20 km, B = 5.40 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 i (b) Number i Units Units B Finish- + C B 35.0 40.0⁰ - Start

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.