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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.
Arc Length for Parametric Equations L = ∫ β α √ ((dx/dt) 2 + (dy/dt) 2 ) dt Note: that we could have utilized the second formula for ds above is we had supposed inste
Advantages and disadvantages of operation researchs
Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and
About Zeros in the Denominator of Rational Expressions One thing that you must be careful about when working with rational expressions is that the denominator can never be zero
Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest
Evaluate the linear equation: Solve the equation ax - b = c for x in terms of a, b, and c. Solution: Step 1. Using Axiom 1, add b to both sides of the equation. a
John was doing his homework on vertical addition, and had to compute : 5 3+ 3 4 and 6 8 +45 He did the first one easily, just the way his teacher had taught him. He first ad
The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find out the width of the rectangle. Let l = the length of the rectangle and let
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The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width? Let x = the width of the rectangle. Let x + 3 = th
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