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Mathematics: Post your doubts here!

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Hello, anyone help me with this number. It's from june 2005p3. Actually, i've been able to prove but the (ii) part , not getting the answer. If you could help me out plus include the explanation, it'd be great. Exams are on friday, and i'm still struggling with vectors II.
 

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Hello, anyone help me with this number. It's from june 2005p3. Actually, i've been able to prove but the (ii) part , not getting the answer. If you could help me out plus include the explanation, it'd be great. Exams are on friday, and i'm still struggling with vectors II.

find normal (n hat) by doing cross product with the direction of line l and the directon vector A.

replace in the formula r. n hat = a . n hat

a can be the point in line equation (4,-2,2)

replace n u get the answer.
 
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Video solution :
 
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for least value of arg z means the smallest angle possible
ths means the tangent to the cricle must be such tht it makes the least possible angle
so u draw the tangent from starting point O to where it makes the least possible angle with the circle
u calculate modulus of z by assuming the tangent the hypotenus of a right angled triangle.
use pythagoras theorem or sin rule if u want.
the O will be the radius of the circle
the H will the moduls of z
use sin rule. its easier.
Thank you!
 
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