1.3 Determines the value of m so that the vectors ū = [-2,6,4] and v = [m,9,6] are: A) collinear B) orthogonal
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- The functions ¢1(x) and ø2(x) are normalized: d φ( (α) φι(α) dx 0(x) 62(x) = 1 = 1 -00 -00 and are mutually orthogonal dx oi(x) $2(x) dx 4i(x) $1(x) = 0 . Is the function b_(x) = ¢1(x) – $2(x) normalized? If not, determine its normalization constant and write the formula for the normalized y_ (x). Is the function +(x) = ¢1(x) + ¢2(x) %3D orthogonal to _(x)?What is the angle θDθDformed by D⃗ (from the picture) and the +x+xaxis? Use counterclockwise to denote positive angles. Answer with 2 significant figures.Evaluate the following: a) [P., A] where A =(P + P3 + P2) 2m
- The figure shows three vectors. Vector A→ has a length of 31.0, vector B→ has a length of 67.0, and vector C→ has a length of 22.0. Find each magnitude and direction. |A→×B→|= ? direction: ? |C→×B→|= ?6. Given vectors Ã= 2â, + 4ây + 10â, and B = -5âp + âo – 3âz, find (a) Ã+ B at P(0, –2,5) , with o = 90° (b) ÷Ē (c) Ã× B (d) The angle between A and B at P (e) The scalar component of A along B at P1.9 Given vectors T = 2a, 6a, + 3a, and S + 2a,+ a₂, find: (a) the scalar projec- tion of T on S, (b) the vector projection of S on T, (c) the smaller angle between T and S. -
- Question: True or False. Why? A vector space must contain at least two vectors. My Comment: I'm confused why this is a question because I believe it to be False. If I draw one vector on a graph with the coordinates (3,5), it is taking up a vector space on an xy coordinate system. Is that incorrect?Consider vectors a = (3, −12) b = (−1, 4)and c = 0. Determine the non-zero scalars ? and ? such that c = ? a + ? b.(6%) Problem 5: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k В = -6. 5i + 7.1j + 10.2k 25% Part (a) What is the x-component of the vector V = 3(A × 2B)? Vx= sin() cos() tan() 7 8 9 НOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 cosh() tanh() cotanh() + END Degrees Radians Vd BACKSPACE DEL CLEAR Feedback Submit Hint I I give up! Hints: 2 for a 0% deduction. Hints remaining: 0 Feedback: 3% deduction per feedback. -This is a cross-product, so the answer will be a vector. In this part, we just want the x-component of the vector. Keep in mind that scalars like "2" and "3" distribute 3.