the way to find out if a vector is perpendicular to a plane the usual way is to find the normal to the plane, then find the cross product of the normal...
Normal vectors for the planes are ( n)_1=(1,1,1) and ( n)_2=(1,-1,1). The normals are not parallel, so neither are the planes. Furthermore, ( n)_1⋅ ( n)_2=1-1+1=1≠q 0, so the planes aren't perpendicular. The angle between them is given by cos θ = (( n...
2 + ˆj + ˆk →B=ˆi+ˆj+ˆk View Solution The unit vactor parallel to the resultant of the vectors→A=4ˆi+3ˆj+6ˆkand→B=−ˆi+3ˆj−8ˆkis :- The angle between the two Vectors→A=3ˆi+4ˆj+5ˆkand→B=3ˆi+4ˆj−5ˆkwill be ...
The direction vectors are {eq}\left\langle {1,... Learn more about this topic: Parallel Lines | Definition & Examples from Chapter 1/ Lesson 11 202K What does parallel mean? Learn about what makes lines parallel, parallel lines examples, ...
If two triangles are similar, then the ratio of side lengths will be constant. It need not be 1 and hence, the side lengths need not be the same. The... Learn more about this topic: Similarity in Geometric Shapes from Chapter 42/ Lesson 3 ...
Given vector a= (2, 0, -5) and vector b= (-3, 6, 2), determine a vector perpendicular to both vectors. Find the scalar and vector projection of the vector b = \left \langle1, 1, -2 \right \rangle onto the vector a = \left \langle3, -4, -1 \right \rangl...
Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. x+y+z=1,x-y+z=1. Please help, what is the angle? That answer says that it should be70.5degrees but I dont know how that a...
A vector can be resolved into many vectors with different magnitudes and directions. Usually, vectors are mainly resolved into three mutually perpendicular vectors along the x, y and z-axis. Consider a vector {eq}\vec{a} {/eq} lying in the x-...
straintg(x,y)=kwhenallfunctionsareC 1 smooth,wecomputethegradientvectors ∇f(x,y)and∇g(x,y)andsolvethesimultaneoussysteminthreevariablesx,y, andλ ∇f(x,y)=λ∇g(x,y)andg(x,y)=k.(1) Thenifthegeometryisright,aconstrainedextremummustoccuratapoint(x 0 ,y 0 ) amongthesolutions...
Hair follicles, mammalian mini-organs that grow hair, miniaturize during aging, leading to hair thinning and loss. Here we report that hair follicle stem cells (HFSCs) lose their regenerative capabilities during aging owing to the adoption of an atypical