Question

Which description of the vector shown is correct? O The magnitude is 777, and the direction angle is approximately 315º. The magnitude is 77, and the direction angle is approximately 135º. O The magnitude is 76, and the direction angle is approximately 315º. O The magnitude is 76, and the direction angle is approximately 135º.​

Answer 1

Step-by-step explanation:

I think the typing of the answer options must have some typos.

the magnitude of a vector is the length of the vector.

the length of the vector is Pythagoras over its coordinates.

this vector goes from (3, -6) to (-4, 1), so the relative vector coordinates are -4 - 3 and 1 - -6 = -7, 7.

so the magnitude of length of the vector is

sqrt((-7)² + 7²) = sqrt(49+49) = sqrt(98)

= 9.899494937...

the direction angle is the angle of the vector with the x-axis.

it is the inverse tan of y/x. and in this case in the second (upper left) quadrant, since the vector is pointing up and left.

the inverse tan of 7/-7 = inverse tab of 1/-1 =

inverse tan of -1 in the second quadrant is 135°.