The dot product of a vector with the vectors i-3k, i-2k and i+j+4k are 0, 5 and 8
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Answer:
Thus, the required vector is 15i + 5j - 3k.
Step-by-step explanation:
Let the required vector be ai + bj + ck.
(ai + bj + ck) . (i - 3j) = 0
a - 3b = 0
⇒ a = 3b ....................... (1)
(ai + bj + ck).(i - 2j) = 5
a - 2b = 5 ......................(2)
From equation (1):
3b - 2b = 5
⇒ b = 5
a = 3 x 5 = 15
(ai + bj + ck).(i + j + 4k) = 8
a + b + 4c = 8
⇔ 15 + 5 + 4c = 8
⇔ 4c = 8-20
⇒ c = -3
Thus, the required vector is 15i + 5j - 3k.
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