Question

For the two vectors A=2î – j and B=i+aſ+3é, perpendicular to each other, find the value of a​

Answer 1

Answer:2

Explanation:here we take dot product of two vector. And we know that when two vectors are perpendicular to each other the their dot product is equal to zero.

By solving this we can find value of a.

Here B=i+aj+3k

Answer 2

Answer:

We know that cross product of any two vectors yields a vector which is perpendicular to both vectors

$</p><p>∴ for \: two \: vectors →A \: and→B if →C is the vector perpendicular to both.</p><p>→C=→A×→B=⎡⎢⎣ˆiˆjˆkA1A2A3B1B2B3⎤⎥⎦</p><p>=(A2B3−B2A3)ˆi−(A1B3−B1A3)ˆj+(A1B2−B1A2)ˆk.</p><p>Inserting \: given \: vectors \: we \: obtain</p><p>→C=⎡⎢⎣ˆiˆjˆk2111−12⎤⎥⎦</p><p>=(1×2−(−1)×1)ˆi−(2×2−1×1)ˆj+(2×(−1)−1×1)ˆk.</p><p>=3ˆi−3ˆj−3ˆk.</p><p></p><p>Now \: unit \: vector \: in \: the direction \: of \:  →C is →C∣∣∣→C∣∣∣</p><p>∴∣∣∣→C∣∣∣=√32+(−3)2+(−3)2</p><p>=√27</p><p>=3√3</p><p>Therefore \: desired unit \: vector \: is</p><p>1√3(ˆi−ˆj−ˆk)</p><p></p><p></p><p>$

Explanation:

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