(We define the cross product only in three dimensions. Solution: Vector Cross Product of the two vectors is calculated using the formula given below a x b = |a| |b| sinθn 1. a x b = 5 * 3 * sin30n 2. a x b = 7.5 n Therefore, the vector cross product of the two vectors is 7.5. Cross product Formula. The cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. The cross product of two vectors and is given by Although this may seem like a strange definition, its useful properties will soon become evident. The magnitude (length) of the cross product equals the area of a parallelogram with vectors a and b for sides: If two vectors are perpendicular to each other, then the cross product formula becomes: The cross product of two vectors are zero vectors if both the vectors are parallel or opposite to each other. A vector has magnitude (how long it is) and direction: Two vectors can be multiplied using the "Cross Product" (also see Dot Product). Then, the thumb of the right hand indicates the direction or unit vector n. With the help of the right-hand rule, we can easily show that the cross product of vectors is not commutative. Cross Product. When a and b start at the origin point (0,0,0), the Cross Product will end at: The cross product could point in the completely opposite direction and still be at right angles to the two other vectors, so we have the: With your right-hand, point your index finger along vector a, and point your middle finger along vector b: the cross product goes in the direction of your thumb. Using the determinant form, we can find the cross product of two vectors, Therefore, \(\vec{X}\times \vec{Y}= 4\vec{i}-3\vec{j}- \vec{k}\). A×B=AB sinθ. 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