Calculus 3 Test 1
calculate. (-5,9)-(8,-3)
(-13,12)
calculate linear combinations 1/2(4,-2,10)-1/3(12,3,3)
(-2,-2,4)
calculate the cross product assuming that u×v=(2,5,0) v×(u+v)
(-2,-5,0)
let v=(6,7,3) which of the following vectors points in the same direction as v? (6,-7,-3) (12,14,6) (3,7,6) (-7,-3,6)
(12,14,6)
find the length to the following vectors: (a) 3i+4j (b) 6i-5j (c) i+j (d) i-5j
(a) 5 (b) √61 (c) √2 (d) √26
compute the dot product (8j+8k) . (i-6k)
-48
calculate the cross product (k+i) × j
-i+k
calculate the cross product. (4i-5j+6k) × (i+j-9k)
39i+42j+9k
If P=(-7,4) and Q= (1,6), find the coordinates of the vector PQ→
PQ→= (8,2)
Find the components of PQ→ P=(5,-1), Q=(9,2)
PQ→=(4,3)
What is the Terminal point Q of the vector a=(1,5) based at P=(6,2)?
Q=(x,y)=(7,7)
calculate the cross product assuming that u × v = (6,5,8) v × u
(-6,-5,-8)
let v=(6,7,3) which of the following vectors is parallel to v? (-7,-3,6) (6,-7,-3) (-6,-7,-3) (3,7,6)
(-6,-7,-3)
Let v=PQ→, where P=(2,1) and Q= (8,-6). Which of the vectors with the following given tails and heads are equivalent to V? (-3,3),(7,10) (0,0),(10,-7) (-1,2),(9,-5) (4,-5),(-6,-12)
(0,0),(10,-7) (-1,2),(9,-5)
find the point of intersection of the lines r(t)=(1,0,0)+t(-3,3,0) and s(t)=(0,1,1)+t(0,0,3)
(0,1,0)
find a vector parametrization r(t) for the line with the given description. passes through (1,1,1) and (6,-5,3)
(1+5t,1-6t,1+2t)
calculate. (5,3)+(9,2)
(14,5)
find the given vector. esubv, where v=(2,5,2)
(2/√33,5/√33,2/√33)
find a vector parametrization for the line passing through P=(3,9,8) with direction vector v=(3,-2,-4). (use t for the paramterized variable.)
(3+3t, 9-2t, 8-4t)
find a vector that is orthogonal to (-3,6,6)
(4,1,1)
calculate. 5(8,6)
(40,30)
find a vector parametrization for the line passing through the origin and the point P=(4,-4,-2). (use t for the paramterized variable.)
(4t,-4t,-2t)
calculate v × w v=(4,3,5), w=(3,1,4)
(7,-1,-5)
find the given vector. unit vector e making an angle of 3π/7 with the x-axis.
(cos(3π/7),sin(3/7))
find a vector parametrization for the line with the given description. perpendicular to the yz-plane, passes through (0,0,4)
(t,0,4)
find v . e where ‖v‖=5, e is a unit vector, and the angle between e and v is 2π/3. v . e
-5/2
calculate the linear combinations 7(4j+2k)-3(2i+7k)
-6i+28j-7k
compute the dot product j . i
0
find the cosine of the angle between the vectors (0,1,4),(2,0,0)
0
let v=i+j+k, and w=7i+8j-5k. compute the dot product. v . w
10
assume that u . v=2, ‖u‖=1, and ‖v‖=3. Evaluate the expression. 7u . (4u-v)
14
compute the dot product. (7,10,10) . (1,0,1)
17
determine whether the two vectors are orthogonal and if not, whether the angle between them is acute or obtuse. (-5,0,-2), (-4,-5,1) orthogonal, acute, or obtuse?
acute
let v=i+6j and w=8j+11k. Find the cosine of the angle θ between v and w.
cos(θ) = 48√5/185
determine whether AB→ is equivalent to PQ→ A=(1,1,1) B=(3,3,3) P=(7,6,4) Q=(9,8,6)
equivalent
determine whether the vectors AB→ and PQ→ are equivalent. A=(15,8), B=(6,8), P=(6,8), Q=(-3,8)
equivalent
determine whether vectors AB→ and PQ→ are equivalent. A=(3,1), B=(7,4), P=(4,-5), Q= (8,-2)
equivalent
find the given vector. unit vector esubv where v=(9,40)
esubv=(9/41,40/41)
determine whether the vectors AB→ and PQ→ are parallel, and if so, determine whether they point in the same direction. A=(1,1), B=(3,4), P=(1,1), Q=(11,16)
parallel in the same direction
Determine whether or not the two vectors are parallel. u=(-4,1,6), v=(8,-2,12)
the vectors are not parallel
let R= (-18,12). calculate the following. the components of u=PR→, where P=(19,16).
u=(-37,-4)
find the vector v=PQ→ P=(1,0,1), Q=(1,4,6)
v=(0,4,5)
find the components and length of the vector v=9i+8j-7k
v=(9,8,-7) ‖v‖=√194
find the given vector. vector w of length 2 in the direction opposite to v=i-j
w=(-√2,√2)
let v=P₀Q₀→, where P₀=(1,-4,3) and Q₀=(0,1,-5). Is the following vector (with tail P and head Q) equivalent to v? P=(1,2,4), Q=(0,7,-4)
yes
find all scalars λ such that λ(2,6) has length 1.
±1/√40
find the angle between v and w if v . w=‖v‖‖w‖.
θ=0
find the angle betwen the vectors. use a calculator if necessary. (5,1,-1) and (1,-3,2)
θ=π/2
let R=(5,3). Calculate the length of OR→.
‖OR‖=√34
find the length of the vector v=(4,3,9)
‖v‖= √106