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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.
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Standard Basis Vectors Revisited In the preceding section we introduced the idea of standard basis vectors with no really discussing why they were significant. We can now do
ABCD is a trapezium AB parallel to DC prove square of AC - square of BCC= AB*
A bricklayer estimates that he requires 6.5 bricks per square foot. He needs to lay a patio that will be 110 square feet. How many bricks will he required? Multiply 6.5 by 110;
Seriation : You have read about a preschooler's ability to order. Ordering a set of objects means to arrange them in a sequence according to some rule. This arrangement could be
tan45 degrees=tan(90degrees-45degrees)
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The area of a parallelogram can be expressed as the binomial 2x 2 - 10x. Which of the following could be the length of the base and the height of the parallelogram? To ?nd out
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Determine the value of a $1800 investment after six years at 9.3% per year, simple interest
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