if the vectors `P = alphahati+alphaj+3hatk` and `Q = alphahati - 2 hatj - hatk` are perpendicular to each other, then the positive value of `alpha` isA. zeroB. `1`C. `2`D. `3`

if the vectors `P = alphahati+alphaj+3hatk` and `Q = alphahati - 2 hat

1.	if the vectors `P = alphahati+alphaj+3hatk` and `Q = alphahati - 2 hatj - hatk` are perpendicular to each other, then the positive value of `alpha` isA. zeroB. `1`C. `2`D. `3`
Answer» Correct Answer - d The scalar praduct of two vectors is given by `overset(vec)(P) .overset(vec)(Q) = PQ cos theta` where `theta` is angle between them Given , `hatP = a hati + a hat j + 3hatk,vecQ = a hati - 2 hatj - hatk` `theta 90^(@)` `:. vecP . vecQ = PQ cos 90^(@) = 0` `(a hati - hatj -3 hatk).(a hati - 2 hatj - hatk) = 0` `a^(2) - 2a - 3 = 0` `rArr a = (2 +- sqrt(4 + 12))/(2) = 3 = 1` Hence position value of a is `3`.

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if the vectors `P = alphahati+alphaj+3hatk` and `Q = alphahati - 2 hatj - hatk` are perpendicular to each other, then the positive value of `alpha` isA. zeroB. `1`C. `2`D. `3`

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