Given that P=(-1,8) and Q=(-2,1), find the component form and magnitude of the vector 3 PQ.
write the vector pq as q-p= -2i+j+i-8j= -i-7j
3pq= -3i-21j
magnitude = square root of(9+441)=15*square root of 2
componentform -3/15*square root of 2i
-21/15*square root of 2j
To find the component form of the vector 3PQ, we need to calculate the difference between the coordinates of point P and Q, and then multiply the resulting vector by 3.
Step 1: Calculate the difference between the coordinates of P and Q:
(Px, Py) - (Qx, Qy)
= (-1, 8) - (-2, 1)
= (-1 - (-2), 8 - 1)
= (-1 + 2, 8 - 1)
= (1, 7)
Step 2: Multiply the resulting vector by 3:
3 * (1, 7)
= (3 * 1, 3 * 7)
= (3, 21)
Therefore, the component form of the vector 3PQ is (3, 21).
To find the magnitude of this vector, we can use the formula:
Magnitude = √(x^2 + y^2)
where x and y are the components of the vector.
Using this formula:
Magnitude = √((3^2) + (21^2))
= √(9 + 441)
= √450
= 21.21 (approx.)
Therefore, the magnitude of the vector 3PQ is 21.21 (approx.).