4 If a = 5i +4j + 2k, b = 4i – 5j + 3k and c= 2i – j- 2k, where i, j, k are the unit vectors, determine: (a) the value of a.b and the angle between the vectors a and b (b) the magnitude and the direction cosines of the product vector (a x b) and also the angle which this product vector makes with the vector c.

Q: Find the unit vector in the direction of v. v = -6.3i + 3.7j = n

A: Topic = Vector

Q: a= b=

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Q: Find the angle between the following pair of vectors. a = (-8, -7,2) and b =(4,-5,-4) a.b cos(8) =…

A: The given problem is to find the dot product of the given vectors and angle between the given…

Q: A vector is A=3i+7j and B vector is B=2i-5j+2k. C vector is C=A+B where ij,k are the unit vectors of…

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Q: Find the angle between the vectors, and

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Q: Find the angle (in radians) between the vectors u and v below. u= 0 1 N N V= IE Give exact…

A:

Q: Suppose only F acts on the object and with this force only, the object experiences a displacement…

A: Introduction: When a force is acted upon an object, there is a displacement. The dot product of the…

Q: Find the angle (in radians) between the vectors u and v below. 1 √√2 u= 0 v= √3 ∙1 Give exact…

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Q: Find the angle a, in radians, between the vectors Q = -2 and 25

A: Given vectors are a = (1, -2, -2) b = (-1, 2, 5)

Q: State the formula relates the dot product of vectors and to their lengths and the angle betwee.…

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Q: 4. Convert the vector (2. 3, 4) into the i and i form. Then find its magnitude of the vector.

A: Vector form of a point (a,b,c) is given by v→=ai+bj+ck and magnitude of this vector is given by,…

Q: Find the angle a in radians between the vectors απ -3] and

A: Step 1: Given vectors: u=[−3−1​] and v=[1−2​] Step 2: To find the angle 𝛼 between two vectors a and…

Q: A vector with initial point at the origin and the terminal point on a unit circle can be written in…

A: Let A and B are the initial and terminal point if a vector then the representation of the…

Q: If vector a= and vector b=, find a · b (the dot product of vector a and vector b).

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Q: The projection of the vector 11i + Aj in the direction of the vector i+3j is the vector 2i+6j. What…

A: To find the value of A for which  Projection of vector (11i + Aj) in the direction of the vector (i…

Q: Vector v = RS has points R(-2, 11) and S(-14, 8). What are the magnitude and direction of RS? Round…

A: Let a point P( x1 , y1 ) and other point Q( x2 , y2 ) Then PQ = ( x2 - x1 )i + ( y2 - y1 )j | PQ | =…

Q: Vectors a, b, and c are given. Determine the vectors (a b)c and (a c)b. Express the vectors in…

A: Given a = i + j b = i - k c = i - 7k

Q: Starting from home at the origin O. a rhino travels for 9.1 km in the direction 60° North of East to…

A: We will use  components along x-axis and y-axis to represent all vectors