1.
If two vectors are perpendicular then A.B=0
[−ki+(i+k)j+9k+k2)k].[(1+k)i+(k+k2)j−kk=0
−k(1+k)+(1+k)(k+k2)+(k+k2)(−k)=0
−k−k2+k+k2+k2+k3−k2−k3=00=0
option 1 is correct
2.
∣A∣=(−k)2+(1+k)2+(k+k2)
=k2+1+k2+2k+k2+k4+2k3
=k4+2k3+3k2+2k+1
∣B∣=(1+k)2+(k+k2)+(−k)2
=1+k2+2k+k2+k4+2k3+k2
k4+2k3+3k2+2k+1
∣A∣=∣B∣
option 2 is correct
3.
if A&B is a unit vector
∣A∣=1, ∣B∣=1
k4+2k3+3k2+2k+1=1k(k3+2k2+3k+2)=0................(1)for k=1
equation (1) not satisfied so option (3) is not correct
4.
∣A∣=1
by equation (1)
k((k3+2k2+3k+2)=0k=0k3+2k2+3k+2=0put k=−1−1+2−3+2=00=0
option 4 is correct
5.
vector is parallel if
−k=d(1+k) & 1+k=d(k(1+k)1+k−k=d, k1=d & k(1+k)=d(−k), d=(−1+k)
Therefore the vectors are not parallel
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