The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector because

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: find the angles between the vectors:x+y=1,2x+y-2z=2

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Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

A:

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: Find a vector that has the same direction as 8i-j+4K but has a length of 6

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Q: a/Find the length and diredtion of the vector 式ド、で Aュ2i+3k where や ノ

A: The given question is from vector and can be solved as shown in step2

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

A:

Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: What is the magnitude of the cross product of two parallel vectors?

A:

Q: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: Express the vector - 4i - 8j + k as a product of its length and direction. - 4i - 8j + k=[Di+ ()j+…

A: To express the vector -4i-8j+k as a product of its length and direction.

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: Express the vector -8i-4j-8k as a product of its length and direction.

A: Given vector v→=-8i-4j-8k

Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: Consider the vectors ā (2, 3, –1) and b = (4, –9, 6). Find the cross product of a and b

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: A n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

A:

Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: when we decompose the vector , what would the vertical component be?

A: Use the decomposing concept of a vector.

Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: If we were to decompose the vector , what would be the vertical component?

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Q: Find the cross products uxv and vxu for the the vectors u = 3i-j-2k and v=i+2j-3k.

A:

Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

A:

Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

A:

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^