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Mathematics : Vector Algebra

Short Answer Type

241. Find the unit vector perpendicular to the vectors

straight a with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space 3 space straight j with hat on top space minus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 3 space stack straight j space with hat on top space minus space 3 space straight k with hat on top.

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242. Find the unit vector perpendicular to vectors

3 straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top comma space space space 2 space straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top

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243. Find the unit vector perpendicular to vectors

4 space straight i with hat on top space plus space straight j with hat on top space space minus space 3 space straight k with hat on top comma space space space space 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top.

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244. Find a unit vector perpendicular to vectors

3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top comma space space 2 straight i with hat on top space plus straight j with hat on top space plus 3 straight k with hat on top

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245. Find a unit vector perpendicular to the plane containing the vectors:

straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space minus space 2 straight k with hat on top space space and space straight b with rightwards arrow on top space equals space straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top

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246. Find a unit vector perpendicular to each of the vector

open parentheses straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses

and

left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis

, where

straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top comma space space space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space plus space space 3 space straight k with hat on top

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Long Answer Type

247.

Find a unit vector perpendicular to each of the vector $straight a with rightwards arrow on top plus straight b with rightwards arrow on top space and space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top comma$ where $straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space plus space 2 straight k with hat on top$ and $straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 straight j with hat on top space minus space 2 space straight k with hat on top.$

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Short Answer Type

248. Find the value of λ so that the two vectors

2 straight i with hat on top space plus space 3 straight j with hat on top space minus straight k with hat on top

and

4 straight i with hat on top plus 6 straight j with hat on top plus straight lambda straight k with hat on top

are (i) parallel (ii) perpendicular to each other.

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Long Answer Type

249.

Find the value of $straight lambda$ so that the two vectors $2 space straight i with hat on top space minus space 4 space straight j with hat on top space plus space straight k with hat on top space space and space 4 space straight i with hat on top space minus space 8 space straight j with hat on top space plus space straight lambda space straight k with hat on top$ are (i) parallel (ii) perpendicular to each other.

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250.

Find the value of $straight lambda$ so that the vectors $2 space straight i with hat on top space plus 4 space straight j with hat on top space minus space 2 space straight k with hat on top$ and $3 straight i with hat on top space plus space 6 straight j with hat on top space plus space straight lambda straight k with hat on top space$ are (i) parallel (ii) perpendicular to each other.

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