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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: vectors help
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amulye (180)

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plz tell me soon ive trying dis for 3 hrs plz reply soon


its time fr u to achive d goal wake up donot hesitate to do hard work
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karthik2007 (3399)

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a = (1,-1)


 


b = (-2,m)


 


For two vectors to be collinear, one should be a scalar multiple of the other, that is, a = kb, where k is some scalar.


 


 


 


So, a = kb => i - j = k(-2i + m)


 


comparing coefficients of i on both sides, 1 = -2k or k = -1/2. Now compare coefficients of j on both sides:


 


-1 = km but k = -1/2, so m = 2.


 


 


 


For the second question, if two vectors are parallel, then their DR's are proportional. For example,


 


if ai + bj + ck and di + gj + hk are to be parallel, then a/d = b/g = c/h.


 


Use this and solve on your own.


Will nip in at times to solve problems :)
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amulye (180)

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c 4 d 1st quesn i 2 got it as 2 but ans is given as even 4 how cud it b possible plz explain anna

its time fr u to achive d goal wake up donot hesitate to do hard work
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RyuAmakusa (680)

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@ amulye these many people have told still u say 4 is given in the ans. then that is wrong see books are not always correct. clearly the slopes of the 2 lines will be diff. if 4 is the ans. so even is u shift as pranay says u wont get 4 it is wrong.and ur second ans is also correct. i got the same. the book ans is again wrong. i am sure
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RyuAmakusa (680)

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@ ayshwarya FIRST u can get the eq of the line through (0,0,0)and
having the direction of (2,-2,1) now SECOND u can find the foot of the perp. droped from P(-4,2,5) to the line let that pt be W now u can find PW vector THIRD find the unit vector in d direction (12,-4,-3) then multiply that with 39 now take the cross product of this vec. and PW vec. take the modulus of the new vec. u have the ans
if u did not know some step say FIRST (how to find the eq) then if u give me the step no. it would be easy to exp.but this is the method of doing it.
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