(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

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Q: B) Determine if the two vectors are orthogonal or parallel or not? A=6i + 6k and B--2i +2j+2k

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Q: Let a = 2 (-) (-3). 1 and b = What is a|²|b²+ la · b|²? -2 be two vectors.

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Q: For the pair of vectors, find U+V, U-V, and 4U+3V U= 2i+5j, V= 5i+2j

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Q: Find values of a and b, for which the following vectors are parallel: (8, a + b, 6), v = (4, 3, 2a —…

A: Given:   u = ⟨ 8 , a+b , 6 ⟩     v = ⟨ 4 , 3 , 2a - b ⟩

Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

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Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

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Q: In the adjoining figure ū and V are unit vectors. Evaluate the following and input your numerical…

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A: Given,

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Q: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

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Q: Use the vectors v=-2i+j and w=4i+3j to find: v + w

A: v=-2i+j and w=4i+3j

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Q: z= 2e'+i

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Q: Find the direction of v:v =(7,-2)

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Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

A: