# a=2i−3j+k, b=2i−4j+5k, c=− i−4j+2k ﬁnd the values of p and q if a+pb+qc is parallel to the x axis You need to replace the given vectors, `bar a, bar b, bar c,` in the equation `a + p bar b + q bar c` , such that:

`a + p bar b + q bar c = 2bar i - 3bar j + bar k + p*(2bar i-4bar j+5bar...

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You need to replace the given vectors, `bar a, bar b, bar c,` in the equation `a + p bar b + q bar c` , such that:

`a + p bar b + q bar c = 2bar i - 3bar j + bar k + p*(2bar i-4bar j+5bar k) + q*(bar i - 4 bar j + 2bar k)`

You need to group the terms containing `bar i, bar j and bar k` , such that:

`a + p bar b + qbar c = (2bar i + 2p*bar i + q*bar i) + ( - 3bar j - 4p*bar j - 4q*bar j) + (bar k + 5p*bar k + 2q*bar k)`

Factoring out `bar i, bar j and bar k,` yields:

`a + p bar b + qbar c = (2 + 2p + q)bar i + (-3 - 4p - 4q)bar j + (1 + 5p + 2q)bar k`

Since `a + p bar b + qbar c` is parallel to x axis, then the coefficients of vectors `bar j` and `bar k` are equal to 0, such that:

`-3 - 4p - 4q = 0 => 4p + 4q = -3`

`1 + 5p + 2q = 0 => 5p + 2q = -1`

Solving the simultaneous equations, yields:

`4p + 4q - 10p - 4q = -3 + 2`

`-6p = -1 => p = 1/6`

Replacing` 1/6` for p in `4p + 4q = -3` , yields:

`4*(1/6) + 4q = -3 => 4 + 24q = -18 => 24q = -22 => q = -22/24 => q = -11/12`

Hence, evaluating p and q, under the given conditions, yields `p = 1/6, q = -11/12.`

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