Question

ii) If v1 = 3i +4j+k and v2=i-j-k,
determine the magnitude of v1 +V2.
Ans: 5​

Answer 1

Answer:

The magnitude of  $\vec v_1+\vec v_2$ is 5

Explanation:

Given vectors

$\vec v_1=3\hat i+4\hat j+\hat k$

And

$\vec v_2=\hat i-\hat j-\hat k$

Therefore,

$\vec v_1+\vec v_2=(3\hat i+4\hat j+\hat k)+(\hat i-\hat j-\hat k)$

$\implies \vec v_1+\vec v_2=(3+1)\hat i+(4-1)\hat j+(1-1)\hat k$

$\implies \vec v_1+\vec v_2=4\hat i+3\hat j+0\hat k$

$\implies \vec v_1+\vec v_2=4\hat i+3\hat j$

Thus magnitude of the vector $\vec v_1+\vec v_2$

$=\sqrt{4^2+3^2}$

$=\sqrt{16+9}$

$=\sqrt{25}$

$=5$

Thus, the magnitude of  $\vec v_1+\vec v_2$ is 5

Hope this helps.

Answer 2

Answer:

The magnitude of \vec v_1+\vec v_2

v

1

+

v

2

is 5

Explanation:

Given vectors

\vec v_1=3\hat i+4\hat j+\hat k

v

1

=3

i

^

+4

j

^

+

k

^

And

\vec v_2=\hat i-\hat j-\hat k

v

2

=

i

^

−

j

^

−

k

^

Therefore,

\vec v_1+\vec v_2=(3\hat i+4\hat j+\hat k)+(\hat i-\hat j-\hat k)

v

1

+

v

2

=(3

i

^

+4

j

^

+

k

^

)+(

i

^

−

j

^

−

k

^

)

\implies \vec v_1+\vec v_2=(3+1)\hat i+(4-1)\hat j+(1-1)\hat k⟹

v

1

+

v

2

=(3+1)

i

^

+(4−1)

j

^

+(1−1)

k

^

\implies \vec v_1+\vec v_2=4\hat i+3\hat j+0\hat k⟹

v

1

+

v

2

=4

i

^

+3

j

^

+0

k

^

\implies \vec v_1+\vec v_2=4\hat i+3\hat j⟹

v

1

+

v

2

=4

i

^

+3

j

^

Thus magnitude of the vector \vec v_1+\vec v_2

v

1

+

v

2

=\sqrt{4^2+3^2}=

4

2

+3

2

=\sqrt{16+9}=

16+9

=\sqrt{25}=

25

=5=5

Thus, the magnitude of \vec v_1+\vec v_2

v

1

+

v

2

is 5

Hope this helps.