CALC 3 Exam 1 Question and answers rated A+ 2025

CALC 3 Exam 1 Question and answers
rated A+ 2025
a · b - correct answers a1(b1)+a2(b2)+a3(b3)
or
|a||b|cosΘ


two vectors are orthogonal if and only if - correct answers a · b = 0


PROJaB - correct answers a · b
−−− a
|a|²


COMPaB - correct answers a · b
---- or |b|cosθ
|a|


a X a = - correct answers 0


a X b · a - correct answers 0


torque - correct answers r X f


|a X b| - correct answers |a||b|sinθ


Volume parallelepiped - correct answers |a(b X c)|

, Vector equation as a sum - correct answers r = r₀ + tv


Vector equation <x, y, z> - correct answers <x₀-ta, y₀-tb, z₀-tc>


line segment r0 to r1 where the segment touches both points - correct
answers r= (1-t)r₀ +tr1


symmetric equations - correct answers x-x₀ y-y₀ z-z₀
----- = ----- = -----
a. b c


Vector equation of the plane - correct answers n · (r-r₀) = 0


Scalar equation of the plane (both) - correct answers a(x-x₀)+b(y-y₀)+c(z-
z₀)=0


or


ax + by + cz + d =0


Distance to plane - correct answers |ax₀+by₀+cz₀+d|
---------------
√(a² +b² + c²)


x². y²