Question

If p 6i 8j and q 4i 3j then calculate unit vector along p 2q

Answer 1

Answer:

I hope it helps.

Explanation:

P=6i+8j

Q=4i-3j

We need to find a unit vector along P+2Q

P+2Q = (6i+8j)+(4i-3j)

P+2Q = 14i+2j

LET,

A = P+2Q = 14i+2j

|A| = 10√2

let 'a' be the unit vector along P+2Q

Then,

a = A/|A|

a = 14i+2j/10√2

a = 2(7i+j)/10√2

a=7i+j/5√2

HENCE THE UNIT VECTOR ALONG P+2Q = a = 7i+j/5√2

Answer 2

Answer:

The unit vector along $\vec p+2\vec q$ is $\frac{7}{5\sqrt{2} } \vec i+\frac{1}{5\sqrt{2} } \vec j$

Explanation:

The proper question is-"If $\vec p=6\vec i+8\vec j$ and $\vec q=4\vec i-3\vec j$,calculate the unit vector along $\vec p+2\vec q$"

The given vectors are

$\vec p=6\vec i+8\vec j\\\vec q=4\vec i-3\vec j$

To find the unit vector along the vector $\vec p+2\vec q$,we need to find the vector first.The vector is found as shown below-

$\vec p+2\vec q=6\vec i+8\vec j+2(4\vec i-3\vec j)=6\vec i+8\vec j+8\vec i-6\vec j\\=14\vec i+2\vec j$

The magnitude of the vector is calculated as shown below

$|\vec p+2\vec q|=\sqrt{14^{2}+2^{2}} =\sqrt{200} =10\sqrt{2}$

For any vector $\vec A$ the unit vector along it is given by the relation as shown below

$\hat A=\frac{\vec A}{|A|}$

Hence the unit vector along $\vec p+2\vec q$ is $\frac{\vec p+2\vec q}{|\vec p+2\vec q|}$

Substituting the vector and its magnitude in the above relation,we get the unit vector as

$\frac{14\vec i+2\vec j}{10\sqrt{2}} =\frac{7}{5\sqrt{2} } \vec i+\frac{1}{5\sqrt{2} } \vec j$

Therefore,the unit vector along $\vec p+2\vec q$ is $\frac{7}{5\sqrt{2} } \vec i+\frac{1}{5\sqrt{2} } \vec j$

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