Given:
a=3i^−pj^+5k^
b=−6i^+14j^+qk^
The vectors are collinear.
For collinear vectors, b=ka where k is a constant.
Using the i^ component:
−6=k×3
k=3−6
k=−2
Using the j^ component:
14=k×(−p)
14=(−2)×(−p)
14=2p
p=214
p=7
Using the k^ component:
q=k×5
q=(−2)×5
q=−10
Therefore, p=7 and q=−10.