Vector A is 3 units length and points along the positive x-axis vector B is 4 units in length and points along negative y-axis .find magnitu

Question

Vector A is 3 units length and points along the positive x-axis vector B is 4 units in length and points along negative y-axis .find magnitude and direction of the vector (a) A+B (b)A-B

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Ngọc Khuê 5 months 2021-09-01T10:39:42+00:00 1 Answers 46 views 0

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    2021-09-01T10:41:07+00:00

    Answer:

    a) < 3 , -4 >

    b) < 3 , -4 >

    Explanation:

    a) If you can imagine this, adding vectors is like putting them “tip to tail”, where you put the beginning point of vector B to the end point of vector A (or vice versa).  Your new vector (A+B) would be from the “tip” of vector A to the “tail” of vector B.

    Mathematically, this is the same as adding the x-components of each vector together as well as the y-components.

    Vector A: 3 units along the positive x-axis: < 3 , 0 >

    Vector B: 4 units along the negative y-axis: < 0 , -4 >

    A+B = < 3 , 0 > + < 0 , -4 > = < (3+0) , (0+(-4)) > = < 3 , -4 >

    b) Subtracting is like adding a negative, so you could use the same “tip to tail” visual by adding the negative of vector B instead (which is B in the opposite direction).

    Vector A: < 3 , 0 >

    Vector B: < 0 , -4 >

    Vector -B: < 0 , 4 >

    A-B = A+(-B) = < 3 , 0 > + < 0 , 4 > = < (3+0) , (0+4) > = < 3 , 4 >

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