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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.
In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR Ans: Since the length of tangents from externa
#how do I add fractions?
The midpoint of the line joining (2a, 4) and (-2, 3b) is (1, 2a +1).Find the values of a & b. (Ans: a = 2, b = 2) Ans : A(2a, 4) P(1, 2a + 1) B(-2,
George worked from 7:00 A.M. to 3:30 P.M. with a 45-minute break. If George earns $10.50 per hour and does not obtain paid for his breaks, how much will he earn? (Round to the near
Evaluate distance traveled by train: A plane flying at 525 miles per hour completes a trip in 2 hours less than another plane flying at 350 miles per hour. What is the distan
calculate the shortest distance between A and B 40degrees west and 50 degrees east respectively laying along 57 degrees north
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Problems Involving Motion - Word Problems: How far can a car travelling at a rate of 52 miles per hour travel in 2½ hours? Solution: Using Equation 13: s = vavt
1. Write down the canonical equations of the line passing through the point A(2,3, 4) and being parallel to the vector q ={5,0,-1}.
is 1 and 1/2+2 and 1/7 3 and 9/4
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