Question #128377
If a=i -j+2k, b = 4j - 2k and c = -10i - 2j +4k
Find the angle between the vectors a and c

Find |a +c |
1
Expert's answer
2020-08-06T17:29:43-0400
θ=cos1(acac)\theta=\cos^{-1}\bigg(\frac{\vec{a}\cdot \vec{c}}{ac}\bigg)

Thus, ac=10+2+8=0    θ=cos1(0)=90\vec a\cdot \vec c=-10+2+8=0\implies \theta=\cos^{-1}(0)=90^\circ



a+c=(i^j^+2k^)+(10i^2j^+4k^)=9i^3j^+6k^    a+c=(9)2+(3)2+62=126\vec a +\vec c=(\hat i-\hat j+2\hat k)+(-10\hat i-2\hat j+4\hat k)=-9\hat i-3\hat j+6\hat k\\ \implies |\vec a +\vec c|=\sqrt{(-9)^2+(-3)^2+6^2}=\sqrt{126}


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