. Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find numbers a, 3 and y such that d= 2i + 3j – k can be expressed in the form d = na + 3b +7e.

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Q: Consider two vectors →A=Ax^i+Ay^j+Az^k and →B=Bx^i+By^j+Bz^k. Scalar product of these two vectors…

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Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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A: Given: u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

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Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

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Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.