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Subtract the corresponding components of vector B from vector A.

Mathematics

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4 parts
a

i + 8j - 8k

b

i + 9j - 15k

c

8i - 7j - 11k

d

9i - 2j - 3k

Step-by-step solution

12 steps

here are the vector calculations for question 6:

Part a· 3 steps

Given A=2i+6j−2kA = 2i + 6j - 2k and B=i−2j+6kB = i - 2j + 6k. Find A−BA - B.

  1. Subtract the corresponding components of vector B from vector A.

    A−B=(2i+6j−2k)−(i−2j+6k)A - B = (2i + 6j - 2k) - (i - 2j + 6k)

  2. Group the components.

    A−B=(2−1)i+(6−(−2))j+(−2−6)kA - B = (2-1)i + (6-(-2))j + (-2-6)k

  3. Perform the subtraction.

    A−B=(1)i+(6+2)j+(−8)kA - B = (1)i + (6+2)j + (-8)k A−B=i+8j−8kA - B = \boxed{i + 8j - 8k}

Part bi + 9j - 15k

Given A=3i−4j−6kA = 3i - 4j - 6k and B=2i−13j+9kB = 2i - 13j + 9k. Find A−BA - B.

  1. Subtract the corresponding components of vector B from vector A.

    A−B=(3i−4j−6k)−(2i−13j+9k)A - B = (3i - 4j - 6k) - (2i - 13j + 9k)

  2. Group the components.

    A−B=(3−2)i+(−4−(−13))j+(−6−9)kA - B = (3-2)i + (-4-(-13))j + (-6-9)k

  3. Perform the subtraction.

    A−B=(1)i+(−4+13)j+(−15)kA - B = (1)i + (-4+13)j + (-15)k A−B=i+9j−15kA - B = \boxed{i + 9j - 15k}

Part c8i - 7j - 11k

Given A=5i−15j−8kA = 5i - 15j - 8k and B=3i+8j−3kB = 3i + 8j - 3k. Find A+BA + B.

  1. Add the corresponding components of vector A and vector B.

    A+B=(5i−15j−8k)+(3i+8j−3k)A + B = (5i - 15j - 8k) + (3i + 8j - 3k)

  2. Group the components.

    A+B=(5+3)i+(−15+8)j+(−8+(−3))kA + B = (5+3)i + (-15+8)j + (-8+(-3))k

  3. Perform the addition.

    A+B=(8)i+(−7)j+(−8−3)kA + B = (8)i + (-7)j + (-8-3)k A+B=8i−7j−11kA + B = \boxed{8i - 7j - 11k}

Part d9i - 2j - 3k

Given A=6i+5j−11kA = 6i + 5j - 11k and B=3i−7j+8kB = 3i - 7j + 8k. Find A+BA + B.

  1. Add the corresponding components of vector A and vector B.

    A+B=(6i+5j−11k)+(3i−7j+8k)A + B = (6i + 5j - 11k) + (3i - 7j + 8k)

  2. Group the components.

    A+B=(6+3)i+(5+(−7))j+(−11+8)kA + B = (6+3)i + (5+(-7))j + (-11+8)k

  3. Perform the addition.

    A+B=(9)i+(5−7)j+(−3)kA + B = (9)i + (5-7)j + (-3)k A+B=9i−2j−3kA + B = \boxed{9i - 2j - 3k}
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