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The direction cosines of a line passing ...

The direction cosines of a line passing through the points `P(-2,4,-5)` and `Q(1,2,3)` and is so directed that it makes an acute angle `alpha` with the positive direction of x-axis, are `3/(sqrt(77)),(-2)/(sqrt(77)),(-8)/(sqrt(77))` 2. `3/(sqrt(77)),(-2)/(sqrt(77)),8/(sqrt(77))` 3. `3/(sqrt(77)),2/(sqrt(77)),(-8)/(sqrt(77))` 4. `3/(sqrt(77)),2/(sqrt(77)),8/(sqrt(77))` 5. `-3/(sqrt(77)),2/(sqrt(77)),8/(sqrt(77))`

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If the direction ratios of a line are proportional to ( 1, -3, 2 ) then its direction cosines are 1/(sqrt(14)),-3/(sqrt(14)),2/(sqrt(14)) b. 1/(sqrt(14)),2/(sqrt(14)),3/(sqrt(14)) c. -1/(sqrt(14)),3/(sqrt(14)),2/(sqrt(14)) d. -1/(sqrt(14)),-2/(sqrt(14)),-3/(sqrt(14))

Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

(4(sqrt(6) + sqrt(2)))/(sqrt(6) - sqrt(2)) - (2 + sqrt(3))/(2 - sqrt(3)) =

Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))+1/(sqrt(6)+sqrt(7))+\ 1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9))=2

(sqrt(2)+sqrt(3))times(sqrt(3)+sqrt(8))

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