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The angles between three non-zero and non coplanar vectors a,b and c are α between b and cand β between c and aand γ between a and b.The vector u and v are defined by u=(aXb)Xc;v=aX(bXc).If u is perpendicular to v, then show that eithera is perpendicular to cor cosβ=cosα.cosγ . solution) Given that u=(axb)xc, v=ax(bxc), both the vectors are equal in magnitude because of the associated law, and u.v=0, therefore it must be true that a.c=0, because excluding a and c , b is not situated at right angles so angle between a and c is 90.
Graph ( x - 2) 2 /9+4(y + 2) 2 = 1 Solution It is an ellipse. The standard form of the ellipse is ( x - h
Determine or find out the direction cosines and direction angles for a = (2, 1, -4) Solution We will require the magnitude of the vector. ||a|| = √ (4+1+16) = √ (21)
What is Trigonometric Ratios ? Trigonometry, a branch of mathematics, is based on the ratios known as sine, cosine, and tangent. Trigonometric ratios apply only to right trian
Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is dierent
1 Data is to be transmitted over Public Switched Telephone Network (PSTN) using 8 levels per signaling elements. If the bandwidth is 3000 Hz, deduce the theoretical maximum transfe
(a) Find an example of groups G, H, K with K H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve
Find the area enclosed between two concentric circles of radii 3.5cm, 7cm. A third concentric circle is drawn outside the 7cm circle so that the area enclosed between it and the 7
cramers rule introduction
fig angles of a irregular polygons exterior and interior .
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