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Q : 31 : Find the unit vector parallel to the resultant of the vectors A = 2i-6j-3k
and B = 4i+3j -k .
Ans :
Resultant of A and B vector => A + B
........ => 6i-3j-4k
Unit vector along A + B vector
= > (A + B) /| A + B |
= > (6i -3j -4k)/√(6^2 +(-3)^2 +(-4)^2)
=> (6i-3j-4k) / √61
Q : 32 Determine the vector which when added to the resultant of A = 2i-4j -6k
and B = 4i+ 3j +3k. gives the unit vector along z -axis.
Ans: 32 Let C be the vector.
C + A + B = k
=> C + (2i-4j-6k) + (4i+3j+3k) = k
=> C = -6i + j +4k
Therefore, Required Vector is C = -6i+j + 4k.
and B = 4i+3j -k .
Ans :
Resultant of A and B vector => A + B
........ => 6i-3j-4k
Unit vector along A + B vector
= > (A + B) /| A + B |
= > (6i -3j -4k)/√(6^2 +(-3)^2 +(-4)^2)
=> (6i-3j-4k) / √61
Q : 32 Determine the vector which when added to the resultant of A = 2i-4j -6k
and B = 4i+ 3j +3k. gives the unit vector along z -axis.
Ans: 32 Let C be the vector.
C + A + B = k
=> C + (2i-4j-6k) + (4i+3j+3k) = k
=> C = -6i + j +4k
Therefore, Required Vector is C = -6i+j + 4k.
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