Vector II Lowersixth Science Mathematics

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Challenging 50-vector problems for 17-year-olds.

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YAKILI LMS

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Vector II Lowersixth Science Mathematics


Froggy Jumps Vector II Lowersixth Science MathematicsOnline version Challenging 50-vector problems for 17-year-olds. by YAKILI LMS 1 What is the distance between P(1,2) and Q(4,6)? a 6 b 4 c 5 2 Distance between (0,0) and (3,4) equals? a 6 b 5 c 7 3 Distance between (−1,−2) and (2,1) is? a 5 b 4 c 7 4 Distance formula uses which operation? a Sum of absolute differences b Cube roots of sums c Square roots of squared differences 5 Angle between vectors a and b is defined by? a Cos theta = (a·b)/(\|a\|\|b\|) b Sin theta = (a·b)/(\|a\|\|b\|) c Tan theta = (a×b)/(\|a\|\|b\|) 6 If a = (1,0) and b = (0,1), angle between them is? a 45° b 90° c 0° 7 Angle between parallel vectors is? a 90° b 0° c 180° 8 Dot product of orthogonal vectors is? a 2 b 1 c 0 9 Unit vector of v = (3,4) is? a (3/5, 4/5) b (5/3, 4/3) c (4/5, 3/5) 10 Unit vector in direction of (−2,0,2) is? a (−1/√2, 0, 1/√2) b (−1, 0, 1) c (−√2, 0, √2) 11 A unit vector has length? a 0 b 1 c ∞ 12 Find the unit vector in direction of (6,8): a (-3/5, -4/5) b (6/14, 8/14) c (3/5, 4/5) 13 Perpendicular vectors satisfy? a \|a×b\| = 1 b \|a\| = \|b\| c a·b = 0 14 If a ⟂ b, then angle is? a 90° b 180° c 0° 15 Find a vector perpendicular to (1,2) in 2D. a (1,−2) b (-2,1) c (2,1) 16 Which operation shows perpendicularity in vectors? a Dot product b Cross product c Sum 17 Two vectors are parallel if a = λb with? a λ = 0 only b λ is a vector c λ is a scalar 18 Direction cosines relate to a vector's? a Magnitude only b Cross product c Angles with axes 19 If v is parallel to w, angle between them is? a 90° b 0° or 180° c 45° 20 Direction cosines are the cosines of angles with? a Vector directions b Planes c X-, Y-, Z-axes 21 Unit vector along (−3, 4, 0) is? a (-5/3, 4/3, 0) b (3/5, -4/5, 0) c (-3/5, 4/5, 0) 22 The magnitude of a vector v is? a \|v\| = sqrt(v1^2+v2^2+v3^2) b \|v\| = v1+v2+v3 c \|v\| = v1v2v3 23 Distance between (1,2,3) and (4,6,3) is? a 5 b 7 c 3 24 Which vectors form a 3D right angle if dot product is 0? a Perpendicular vectors b Same vectors c Parallel vectors 25 If a and b are parallel, a·b equals? a a×b b 0 c \|a\|\|b\| 26 If a = (2,0,0) and b = (0,3,0), angle is? a 90° b 45° c 0° 27 Distance formula in 3D uses? a Sum of differences b Sum of squared differences, rooted c Product of coordinates 28 Unit vector is of length? a 0 b 1 c 2 29 Direction cosines are cosines of angles with? a Vector magnitudes b Coordinate axes c Planes 30 A perpendicular to (1,2,2) could be? a (1,2,2) b (-2,1,0) c (2,1,0) 31 Angle between (1,1,0) and (1,0,1) is? a 90° b 0° c 60° 32 The dot product of unit vectors equals? a Product of magnitudes b Sum of components c Cosine of angle between them 33 If a and b are not zero and parallel, a·b equals? a \|a\|+\|b\| b \|a\|\|b\|cos0 = \|a\|\|b\| c 0 34 Unit vector in direction of (0,0,5) is? a (0,0,1) b (1,0,0) c (0,0,5) 35 Cosine of angle between a and b is given by? a (a·b)/(\|a\|\|b\|) b \|a×b\| c \|a\|\|b\|/(a·b) 36 If v = (a,b,0) and w = (0,a,b), angle is? a Always 0° b Depends on a,b c Always 90° 37 Find direction cosines for vector (x,y,z). a l=m=n=1 b l=x, m=y, n=z c (l,m,n) with l=x/\|v\|, etc 38 Distance formula generalizes to? a Only 2D b Only 3D c n-dimensional space 39 Perpendicular and parallel vectors relationship? a They are distinct cases b Same concept c Always equal 40 Given a and b, to check parallel, compare ratio of components. a Yes, proportional components b Check sum of components c Check cross product only 41 Angle between opposite vectors is? a 0° b 90° c 180° 42 Normalizing a vector yields a? a Unit vector b Quaternion c Scalar 43 What is the unit vector of (−6,8,0)? a (-3/5, 4/5, 0) b (-6/8, 8/8, 0) c (3/5, -4/5, 0) 44 Distance between (0,0) and (−3,−4) is? a 6 b 5 c 7 45 Angle between a and itself is? a 0° b 180° c 90° 46 A unit vector must have length? a 1 b 0 c 2 47 Two vectors are parallel when their cross product is? a Non-zero b One vector c Zero vector 48 Direction cosines are related to? a Magnitudes b Angles with axes c Areas 49 What is the distance in 2D for (2,3) to (5,7)? a 5 b 6 c 7 50 If v = (1,2,3) and w = (4,5,6), angle cos = a (v×w)·(1,1,1) b (\|v\|+\|w\|) c (1•4+2•5+3•6)/(\|v\|\|w\|)

Vector II Lowersixth Science Mathematics

Froggy Jumps

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Vector II Lowersixth Science MathematicsOnline version

by YAKILI LMS

What is the distance between P(1,2) and Q(4,6)?

Distance between (0,0) and (3,4) equals?

Distance between (−1,−2) and (2,1) is?

Distance formula uses which operation?

Angle between vectors a and b is defined by?

If a = (1,0) and b = (0,1), angle between them is?

Angle between parallel vectors is?

Dot product of orthogonal vectors is?

Unit vector of v = (3,4) is?

Unit vector in direction of (−2,0,2) is?

A unit vector has length?

Find the unit vector in direction of (6,8):

Perpendicular vectors satisfy?

If a ⟂ b, then angle is?

Find a vector perpendicular to (1,2) in 2D.

Which operation shows perpendicularity in vectors?

Two vectors are parallel if a = λb with?

Direction cosines relate to a vector's?

If v is parallel to w, angle between them is?

Direction cosines are the cosines of angles with?

Unit vector along (−3, 4, 0) is?

The magnitude of a vector v is?

Distance between (1,2,3) and (4,6,3) is?

Which vectors form a 3D right angle if dot product is 0?

If a and b are parallel, a·b equals?

If a = (2,0,0) and b = (0,3,0), angle is?

Distance formula in 3D uses?

Unit vector is of length?

Direction cosines are cosines of angles with?

A perpendicular to (1,2,2) could be?

Angle between (1,1,0) and (1,0,1) is?

The dot product of unit vectors equals?

If a and b are not zero and parallel, a·b equals?

Unit vector in direction of (0,0,5) is?

Cosine of angle between a and b is given by?

If v = (a,b,0) and w = (0,a,b), angle is?

Find direction cosines for vector (x,y,z).

Distance formula generalizes to?

Perpendicular and parallel vectors relationship?

Given a and b, to check parallel, compare ratio of components.

Angle between opposite vectors is?

Normalizing a vector yields a?

What is the unit vector of (−6,8,0)?

Distance between (0,0) and (−3,−4) is?

Angle between a and itself is?

A unit vector must have length?

Two vectors are parallel when their cross product is?

Direction cosines are related to?

What is the distance in 2D for (2,3) to (5,7)?

If v = (1,2,3) and w = (4,5,6), angle cos =