GTU IMP MCQ Material With Mock Test Material For Mathematics Chapter Vector, GTU MCQ Quiz Solution Or Book Material One-Click Download Now
Applied Mathematics Chapter Vector (Q&A)
1. ____________ of the following is unit vector.
Answer : (`\frac{1}{\sqrt{2}}`, `\frac{1}{\sqrt{2}}`)
2. | 3i̅ - 4j̅ + 5k̅ | = ______.
Answer : `5\sqrt2`
3. Magnitude of x̅ = 3i̅ + 2j̅ - 3k̅ is ______.
Answer : `\sqrt{22}`
4. If x̅ = (2, 1) and y̅ = (-1, 3) then 2 x̅ + 3 y̅ = ____________.
Answer : (1, 11)
5. If a̅ = (3, 7, 2) and b̅ = 2i̅ + 5j̅ - 2k̅ then |a̅ + b̅ | = __________.
Answer : 13
6. If a̅ = (2, 1, -1) and b̅ = (1, -3, 2) then |2a̅ - 3b̅ | = _______.
Answer : `\sqrt{186}`
7. If vectors x̅ = (k, 2, -3) and y̅ = (`\sqrt{k}`, `\sqrt{13}`, 0) are of same magnitude then k =
Answer : 0 OR 1
8. If x(1, 2) + y(2, 1) = (3, 3) then x + y = ______.
Answer : 2
9. Direction angle of the vector x = j̅ + k̅ are _____.
Answer : `\frac\pi2,\frac\pi4,\frac\pi4`
10. If x̅ = (3, 2, 1) and y̅ = (1, 2, -1) then x̅ • y̅ = _______.
Answer : 6
11. (3j - 2k + i) • ( 5k̅ + 3j̅ +2i̅ ) = ________.
Answer : 1
12. If x̅ = (secθ, tanθ, -1) and y̅ = (secθ, -tanθ, 1) then x̅ • y̅ = _______.
Answer : 0
13. The value of i̅ • j̅ + j̅ • k̅ + k̅ • i̅ is __________.
Answer : 0
14. If (1, -3, 4) • (1, k, -4) then k = ________.
Answer : 5
15. If x̅ = (k, 4, 2k) and y̅ = (2k, -1, k) then are mutually perpendicular then k = ___________.
Answer : `\pm`1
16. If x̅ = i̅ + j̅ - k̅ and y̅ = 2j̅ - k̅ + i̅ then x̅ • y̅ = ________.
Answer : 4
17. If x̅ = (1, 3, -2) and y̅ = 4 i̅ - 2j̅ - k̅ then x̅ ^ y̅ = ________.
Answer : 90°
18. If x̅ = (1, 2, 1) and y̅ = (1, -1, 1) then (x̅ + y̅) • (x̅ - y̅) =...
Answer : 3
19. If |x̅| = 4 then x̅ • (5 • x̅ ) = ________.
Answer : 80
20. If x̅ × y̅ = (1, -2, -5) then y̅ × x̅ = _______.
Answer : y̅ × x̅ = (-1, 2, 5)
21. x̅ × (x̅ - y̅) = ________.
Answer : y̅ × x̅
22. If x̅ = (1, 2, 3) and y̅ = (-1, 3, 5) are given vector then x̅ × y̅ =...
Answer : x̅ × y̅ = (1, -8, 5)
23. If x̅ = (2, 2, -1) and y̅ = (6, -3, 2) then x̅ × y̅ =...
Answer : x̅ × y̅ = (-1, 10, 18)
24. A unit vector a long 3i + 4j is ______.
Answer : 5
25. ( i̅ - 2j̅ + 2k̅ ) = ________.
Answer : 3
26. If x(1, 1) + y(2, 1) = (3, 2) then (x, y) = _______.
Answer : 1
27. a̅ = - i̅ + 3j̅ , then |a̅| = _____.
Answer : `\sqrt{10}`
28. If a̅ = -2i + 3j + k , b̅ = 2i - 3j + 2k̅ then a̅ + b̅ = _______.
Answer : (0, 0, 3)
29. If a̅ = 2i + j + k , b̅ = i - j + 3k̅ then a̅ • b̅ = _______.
Answer : 4
30. a̅ = 2i + 3j - k , b̅ = 4i + 6j - 2k̅ then a̅ × b̅ = _______.
Answer : 0
31. a̅ = i + j, b̅ = j - k̅ then angle between a̅ and b̅ = _______.
Answer : 0
32. (a̅ × b̅) • (b̅ × a̅) = _______.
Answer : (a̅ × b̅)²
33. a̅ • (a̅ × b̅) = _______.
Answer : 0
34. a̅ • a̅ = ______.
Answer : |a̅|²
35. b̅ • b̅ = _______.
Answer : 0
36. If two forces (3i - j + 2k), (i + 3j -k) are applied on a particle , it's moves from (2i + 3j+ k ) to the point (5i + 2j +3k) then find the work done by three force.
Answer : W = 12 Units
37. If 2i + 3j -k and pi - j + 3k are perpendicular each other then find the value of p.
Answer : P = 3
38. If a̅ = (p, 2, 1) and b̅ = (2, p, -4) are perpendicular each other then find the value of p.
Answer : P = 1
39. If a̅ = (2, 3, -1) and b̅ = (x, -1, 3) are perpendicular each other then find the value of x.
Answer : x = 0
40. Find the unit vector perpendicular to the plane containing the vector a̅ = i̅ - j̅ + k̅ and b̅ = 2i̅ + 3j̅ - k̅.
Answer : `\frac{1}{\sqrt{38}}`, (-2, 3, 8)
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