Class 12

Math

Algebra

Vector Algebra

For given vectors, $a=2i^−j^ +2k^$ and $b=−i^+j^ −k^$ find the unit vector in the direction of the vector $a+b$.

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Show that $∣a∣b+∣∣ b∣∣ a$ is a perpendicular to $∣a∣b−∣∣ b∣∣ a,$ for any two non-zero vectors $aandb˙$

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Vectors $aandb$ are non-collinear. Find for what value of $n$ vectors $c=(n−2)a+bandd=(2n+1)a−b$ are collinear?

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If the vectors $aandb$ are linearly idependent satisfying $(3 tanθ+1)a+(3 secθ−2)b=0,$ then the most general values of $θ$ are a. $nπ−6π ,n∈Z$ b. $2nπ±611π ,n∈Z$ c. $nπ±6π ,n∈Z$ d. $2nπ+611π ,n∈Z$