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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.
If a school has lockers with 50 numbers on each combination lock, how many possible combinations using three numbers are there.
One of two complementary angles is 80& of the other. What is the degree measure of the smaller angle?
21-83/4
Differentiate following functions. h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows. h (t )
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
Polar Coordinates Till this point we've dealt completely with the Cartesian (or Rectangular, or x-y) coordinate system. Though, as we will see, this is not all time the easie
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
What is log3(x+1)
2+4
how do u add them together?
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