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Find the scalar and vector projections of $ b $ o…

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Problem 41 Medium Difficulty

Find the scalar and vector projections of $ b $ onto $ a $.

$ a = \langle 4, 7, -4 \rangle $ , $ b = \langle 3, -1, 1 \rangle $


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Related Courses

Calculus 3

Calculus: Early Transcendentals

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

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Video Transcript

The problem is find the scaler and the factor. Productions of b into a a is equal to 47 negative 4 b is equal to 3 negative, 1 and 1 point so first, the magnitude of a is equal to but 16 plus 49 plus 16 point. This is equal to 9, then be half the scatter projections of b into a this is equal to a dot b over the magnitude of a so. This is equal to 12 minus 7 minus 4 over 9 point. So this is equal to 1 over 9. Then the projection work, the projections of b into a is equal to 1 over 9 times victor over the magnitude of a point. This is equal to 1 over 81 o times 47 negative 4 point. This is equal to 4 over 817 over 81 and negative 4. Over 8.

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