Question

6i^+2j^k^ find the magnitude of the vector​

Answer 1

Answer:

Figure 1: The magnitude of the vector v = 6i + 2j + 3k

The magnitude of the vector v, written v or v, is the length of the arrow representing v. In Figure 1, the vector v=6i+2j+3k is shown in blue. Its magnitude is the length OP. By Pythagoras in the triangle OBP, we have that OP^2=OB^2+BP^2. But by Pythagoras in the triangle OAB, we have that OB^2=OA^2+AB^2. Putting these together, we have that

OP2 = = = OA2+AB2+BP2 62+22+32 49

and therefore that v=49=7 .

In general, the magnitude of the vector a1i+a2j+a3k is a21+a22+a23 . This is sometimes called the modulus of the vector.