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Find the dot product v middot w and the angle between v and w. v= -4i + 2j + k,w=i + 4j + 4k v middot w = (Simplify your answer. Type an exact value, using radicals as needed.) The angle between v and w is theta = degree. (Do not round until the final answer. Then round to the nearest tenth as needed.)

On the slide of the testis, the (A) is easily seen as it delimits the organ. From there, it invaginates and produces many lobules which house 1-4 (B) each. On another slide of the testis, now at a magnification of 400X, each of these structures can be seen to contain a (C) epithelium. Starting at the periphery of these structures, the meiosis process can be followed revealing each of the 4 stages: (D), (E), (F) and (G) to create the gamete (H) as the final product This cell is released in the lumen to flow with the help of the (I) fluid onto the next organ called (J). Two other cells are integral to this process: the (K) which maintain the blood-testis barrier and the (L) which produce the testosterone. On the slide of the next organ (what you wrote for J), notice a pseudostratified columnar epithelium comprised of both (M) cells with stereo cilia and large nuclei and (N) cells of very small size. In this long tube, the gametes mature. The (O) in the wall contract and helps bring the gamete onto the next organ called (P). On this slide, notice a very large (Q) to help move the gametes into the next organ called (R). The latter (organ) seen on this slide, is separated into 3 sections according to what it passes through: the first segment called (S) passes through the prostate, the second segment called (T) passes through the urogenital diaphragm and finally the third segment called (U) passes through the penis. Amongst the 3 accessory glands, only one is given to observe in the lab. This slide represents the (V) which as you will notice, is a collection of smaller (W). The other two accessory glands include the (X) which are the first to add their secretion to the sperm and the other accessory being the (Y) glands, which are last to add their secretion in the form of mucus. The intromission organ called the (Z) and seen also on a previous slide, houses 3 sections of a unique type of erectile tissue: these are named (AA) (in 2 sections) and (BB) (in 1 section). On the slide of the gamete, you can observe this unique motile cell which uses its (CC) to move around and the darkly ovoid shaped anterior end housing the (DO). On the slide of the ovary, one can observe an outer (EE) housing the various gametes in development and an inner (FF) containing fundamental vasculature. Similarly to the male reproductive system, the meiosis process (denoted on 3 different slides) can be folowed revealing each of the 4 stages denoted by the development of the follicles bringing it up to the ovulation: (GG), (HH), (I) and (JJ) to create an incomplete gamete called (KK) as the final product before any potential fertilization occurs. This cell is released into the abdominal cavity area to be captured by this next organ called (LL) and as seen on this slide. The remnants of the follicle left behind in the ovary will be kept if fertilization occurs (which will than be called (MM) as seen on this slide) and not kept if fertilization does not take place (which will than be called (NN) which is seen on this slide). Continuing on the pathway, this organ (as seen in a previous slide) houses a simple columnar ciliated epithelium made of very special cells called (OO) which have the important function of providing nutrients to any of the passing gametes. From there, these nourished gametes are transported to the next Urge sized organ called the (PP) as observed on this slide. This is where the developing embyolfoetus stays and develops. The biggest layer of the wall that can be observed is the (QQ) which contracts to deliver the baby once the pregnancy has ended. In an every day setting, this organ undergoes the development of its (RR). The latter which is its inner layer will grow in preparation of a potential' new individual having to use 1L But when no fertilization takes place, the (SS) of the (RR) sloughs off and the process repeats itself in a monthly cycle. The next slide depicts the organ that leads to the exterior of the body. It is called the (TT) and is lined by this type of epithelium (UU). Lastly 2 accessory components can be observed: on this slide, the (W) can be observed and represents the fetal-maternal exchange organ only produce when a pregnancy occurs and on this slide, the (WW) which are responsible for the production of milk to feed the developed baby. A lot of (XX) tissue can be observed here as it goes into the production of the milk. Lastly, before any pregnancy period of an individual female, the (WW) are not fully developed. Thus on this slide, you can observe various areas which contain stem cells that will develop into secreting alveoli upon endocrine stimulation and the pregnancy setting.

Given v = - i - j and w = i + j (a) find the dot product v middot w; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal, or neither. (a) v middot w =