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# the acute angle in degrees that makes a with c, when a=4i+0j+k , c=i+j+3k

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the acute angle in degrees that makes a with c, when a=4i+0j+k , c=i+j+3k

Guest Aug 27, 2014

#1
+80935
+10

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(42 + 02 + 12) =√(16 + 1) = √17

And the magnitude of c  = √(12 + 12 + 32) =√(1 + 1 + 9) = √11

And the angle is given by

cos-1 (a(dot)c / (llall * llcll)  = cos-1 ((7) / (√17 * √11) = cos-1 ((7) / (√187) = cos-1 (0.5118906968889915) = about  59.2°

CPhill  Aug 27, 2014
Sort:

#1
+80935
+10

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(42 + 02 + 12) =√(16 + 1) = √17

And the magnitude of c  = √(12 + 12 + 32) =√(1 + 1 + 9) = √11

And the angle is given by

cos-1 (a(dot)c / (llall * llcll)  = cos-1 ((7) / (√17 * √11) = cos-1 ((7) / (√187) = cos-1 (0.5118906968889915) = about  59.2°

CPhill  Aug 27, 2014

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