Vector Calculus Answers

Given that a = 5i +2j - k and b = I - 3j + k. Find (a + b) x (a + b).

2i - 12j - 34k
2i + 12j + 34k
2i -3j + 12j
2i + 2k

A ...... line AB occurs when the point A is fixed.

free vector
position vector
force
null vector

Find the vector product axb. If a = 2i + 3j + 4k and b = 5i - 2j + k

11i + 18j - 19k
2j + 3k
5i - 6j + 7k
4i - 6j +11k

Given that :
r−1=6i−8j+2k,r2=4i+5j+7k,r3=−2i+j+6k is a vector.Find r1 r2

30
26
-26
19

If
r4=r1+r2+r3
,which of the vectors are linearly dependent .

r1
r3
r4
r2

What type of vector is w+(-w)=0

null vector
scalar vector
vector
magnitude

For the vectors □(□(→┬a )) =xyz□(→┬i )-2xz^2 □(→┬j )+xz□(→┬k ) and □(→┬b )=2z□(→┬i )+y□(→┬j )-x□(→┬k)
Find ∂^2/∂x∂y (□(→┬a )×□(→┬b )) at (2,0,-1)

Find the angle between the lines whose direction cosines are given by the equations.
(i) l + 2m +3n = 0 and 3lm – 4ln + mn = 0
(ii) l + m + n = 0 and l2 + m2 – n2 = 0

Prove that in any triangle the line joining the mid-points of any two sides is parallel to the third side and half of its length.

The vectors □(→┬a ) and □(→┬b ) are non-collinear. Find for what value of x, the vectors □(→┬c )=(x-2) □(→┬a )+□(→┬b ) and □(→┬d ) =(2x+1) □(→┬a )- □(→┬b ) are collinear.