If the vectors `xhati - 3hatj + 7 hatk` and `hati + y hatj- z hatk` are colliner then the value of `(xy^(2))/(z)` is equla .
If the vectors `xhati - 3hatj + 7 hatk` and `hati + y hatj- z hatk` are colliner then the value of `(xy^(2))/(z)` is equla .
A. `(9)/(7)`
B. `(-9)/(7)`
C. `(-7)/(9)`
D. `(7)/(9)`
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Correct Answer - B
Given, vectors `x hat(i) - 3 hat(j) + 7 hat(k)` and `hat(i) + y hat(j) - z hat(k)` are collinear
`:. (x)/(1) = (-3)/(y) = (7)/(-z) = k`
`implies x = k, - 3 = ky` and 7 = - kz
Now, `(xy^(2))/(z) = (k(-(3)/(k))^(2))/(((-7)/(k))) = ((9)/(k))/((-7)/(k)) = (-9)/(7)`
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