Question

Suppose that a = 2i + j, b = i − 4j + k, and c = j + k. What is the magnitude of the vector 2a − b + c ?

Answer 1

Explanation:

2a = 4i + 2j

-b = -i +4j -k

c = j + k

thus, 2a - b + c = (4i +2j) + ( -i+4j-k) +(j+k)

then, 2a -b +c = 3i +7j

Answer 2

Answer:

Magnitude of vector is $\sqrt{90} units$.

Explanation:

Given,

$a = 2i + j$

$b = i-4j + k$

$c = j + k$

To find :

Magnitude of vector : $2a-b+c$

$2a-b+c$ $= 2(2i+j)-(i-4j+k)+ j+k$

                 $= 4i+4j-i+4j-k+j+k$

                  $= 3i+ 9j$

Magnitude of vector is given by,

$= \sqrt{3^{2}+ 9^{2} }$

$= \sqrt{9+ 81} \\=\sqrt{90 } units$

Therefore, magnitude of vector is $\sqrt{90} units$.

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