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Find a unit vector that has the same direction as the given vector. −3i 7j

User Thmspl
by
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2 Answers

5 votes

Final answer:

To find a unit vector with the same direction, divide the given vector by its magnitude and simplify.

Step-by-step explanation:

To find a unit vector that has the same direction as the given vector -3i + 7j, we need to divide the given vector by its magnitude. The magnitude of a vector is found using the formula sqrt(x^2 + y^2), where x and y are the coefficients of i and j respectively in the given vector.

The magnitude of the given vector is sqrt((-3)^2 + 7^2) = sqrt(9 + 49) = sqrt(58).

Therefore, the unit vector that has the same direction as the given vector is (-3/sqrt(58))i + (7/sqrt(58))j.

User Ievche
by
8.0k points
6 votes
The unit vector has the same direction of the given vector but its magnitude is 1.

To find the unit vector divide by the magnitude of the given vector.

Vector - 3i + 7j

Magnitude = |-3i + 7j| = √(3^2 + 7^2) = √(9 + 49) = √58 = 7.62

Then the unit vector is: (-3/√58) i + (7/√58) j
User KyriakosSt
by
8.9k points

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