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Vector Algebra

Question
CBSEENMA12035698
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If space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space perpendicular space vectors comma space open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar space equals space 13 space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 5 space and space find space the space value space of space open vertical bar straight b with rightwards arrow on top close vertical bar.

Solution

Given that straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two perpendiculars vectors.
Thus, straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0
Also given that, open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar equals 13 space and space open vertical bar straight a with rightwards arrow on top close vertical bar equals 5.
We need to find the value of straight b with rightwards arrow on top.
Consider open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar squared colon
open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar squared space equals space open vertical bar straight a with rightwards arrow on top close vertical bar squared plus 2 open vertical bar straight a with rightwards arrow on top. straight b with rightwards arrow on top close vertical bar plus open vertical bar straight b with rightwards arrow on top close vertical bar squared 13 squared space equals space 5 squared plus 2 cross times 0 plus open vertical bar straight b with rightwards arrow on top close vertical bar squared 169 space equals 25 plus open vertical bar straight b with rightwards arrow on top close vertical bar squared open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals 169 minus 25 open vertical bar straight b with rightwards arrow on top close vertical bar squared space equals 144 straight b with rightwards arrow on top space equals space 12

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