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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.
Terry earns $680 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.
Determine if the three vectors a → = (1, 4, -7), b → = (2, -1, 4) and c → = (0, -9, 18) lie in similar plane or not. Solution Thus, as we noted prior to this example al
2 of 10 =
sin(2x+x)=sin2x.cosx+cos2x.sinx =2sinxcosx.cosx+(-2sin^2x)sinx =2sinxcos^2+sinx-2sin^3x =sinx(2cos^2x+1)-2sin^3x =sinx(2-2sin^2x+1)-2sin^3
what is 5+10
What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin
From the top of a 200 m lighthouse, the angle of depression to a ship in the ocean is 23 . How far is the ship form the base of the lighthouse?
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball , determine the number of blue balls in the bag.
One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti
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