Let u be a vector coplanar with the vectors a=2i^+3j^−k^ and b=j^+k^ If u is perpendicular to a and u.b=24 then ∣u∣2 is equal to
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Show that the points A, B and C with position vectors, a=3i^−4j^−4k^, b=2i^−j^+k^and c=i^−3j^−5k^ respectively form the vertices of a right angled triangle.
Let a,band cbe three vectors such that ∣a∣=3,∣∣b∣∣=4,∣c∣=5and each one of them being perpendicular to the sum of the other two, find ∣∣a+b+c∣∣.
Show that each of the given three vectors is a unit vector: 71(2i^+3j^+6k^),71(3i^−6j^+2k^),71(6i^+2j^−3k^)Also, show that they are mutually perpendicular to each other.
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Find the projection of the vector i^+3j^+7k^on the vector 7i^−j^+8k^
Show that the points A(2i^−j^+k^),B(i^−3j^−5k^),C(3i^−4j^−4k^)are the vertices of a right angled triangle.
If a is a unit vector and (x−a).(x+a)=8, then find ∣x∣
Find the angle between the vectors i^−2j^+3kand 3i^−2j^+k