State whether the following relations are true or false
(1)`vec(AB)=vec(BA)`
(2)`vec(AB)=-vec(BA)`
(3)`|vec(AB)|=|vec(BA)|`
(4)`|vec(AB)|=|-vec(AB)|`
(5)`hatj=hatk`
(6)`|hatj|=|hatk|`
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`A , B , Ca n dD` are any four points in the space, then prove that `| vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4` (area of ` A B C` .
Let P.V of A,B, C d and D be `veca, vecb,vecc and vec0` , respectively. Then `vec(AB)xxvec(CD)=(vecb-veca)xx(-vecc), vec(BC)xxvec(AD)=(vecc-vecb)xx(-veca)` `vec(CA)xxvec(BD)=(veca-vecc)xx(-vecb)` `vec(AB)xxvec(CD)+vec(BC)xxvec(AD)+vec(CA)xxvec(BD)` `veccxxvecb+vecaxxvecc+vecaxxvecc+vecbxxveca-vecaxxvecb+veccxxvecb` `2(veccxxvecb+ vecbxxvecbxxveca+vecaxxvecc)` `2(veccxx(vecb-veca)-vecaxx(vecb-veca))` `= 1(vec(AC)xxvec(AB))` `|vec(AB)xxvec(CD)+vec(BC)xxvec(AD)+vec(CA)xxvec(BD)|=4|1/2(vec(AC)xxvec(AB))|=4triangleABC`
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Read the extract and state whether the following statements are true or false. Correct the false statements. (a) Growing in abundance
(a) False. The quality of the crop is more important than growing in abundance a lesser variety of crop. (b) True (c) False. The author was successful in finding Kasbai from an Adivasi woman at Boripada, a...
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6) Angle between vector \( \vec{A}=\vec{\imath}+2 \vec{\jmath}-\vec{k} \) and \( \vec{B}=-\vec{\imath}-2 \vec{\jmath}+\vec{k} \) will be.. a)zero \( \begin{array}{ll}\text { b) } 45^{\circ} & \text { c) } 90^{\circ}\end{array} \) d) \( 180^{\circ} \)
Given \(\vec A\) = \(\hat i+2\hat j-\hat k\) \(\vec B\) = \(-\hat i-2\hat j+\hat k\) Angle b/w \(\vec A\) and \(\vec B\) cos θ = \(\frac{\vec A.\vec B}{|\vec A|.|\vec B|}\) \(=\frac{(\hat i+2\hat j-\hat k).(-\hat i-2\hat j+\hat k)}{\sqrt{1^2+(2)^2+(1)^2}\sqrt{(-1)^2+(-2)^2+(1)^2}}\) cos θ = \(\frac{-1-4-1}{\sqrt6\times\sqrt6}\) cos θ = -6/6 cos θ = -1 θ = 180° option...
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State whether the following statements are true or false. Correct the false statement. (i) The people of America did not think
(i) True (ii) False – So many objections were raised by the laity to the word ‘nation’. (iii) False – Politically-minded Indians resented the expression ‘the people of India’. (iv) True
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State whether the following statements are True or False. Correct the false statements by finding
(a) False. The cherry tree took eight years to grow into a six-feet high full-grown, fruit-bearing tree. (b) True (c) True (d) False. The underlying message in this poem is not about the importance of trees. It...
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State whether the following statements are True or False and correct the false statements.
(i) False. They damaged the cherry sapling but could not destroy it as it had a violent urge to move ahead. (ii) True (iii) True
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State whether the following statements are true or false. Correct the false statement. (i) The dentist removes all the teeth
(i) False. The dentist only removes the rotting, useless teeth. (ii) False. Mathematics help in the alignment of buildings and roads, with precision. (iii) False. Planners have no concern for the nature and...
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Find `vec(A).vec(b)` when (i) `vec(a)=hat(i)-2hat(j)+hat(k)` and `vec(b)=3 hat(i)-4 hat(j)-2 hat(k)` (ii) `vec(a)=hat(i)+2hat(j)+3hat(k)` and `vec(b)=
Correct Answer - (i) 9 (ii) 8 (iii) -7
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If `vec(a)=(2hat(i)-hat(j)+hat(k)), vec(b)=(hat(i)-3hat(j)-5hat(k)) and vec(c)=(3hat(i)-4hat(j)-hat(k))`, find `[vec(a)vec(b)vec(c)]` and interpret th
Correct Answer - 0, the given vectors are coplanar
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Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \). Which one of the following is correct ? [IIT-2007] (a) \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}=\overrightarrow{0} \) (b) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ c } \times \overrightarrow{ a } \neq \overrightarrow{0} \) (c) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ a } \times \overrightarrow{ c } \neq \overrightarrow{0} \) (d) \( \vec{a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a} \) are mutually \( \perp \)
Given that \(\vec a, \vec b\) and \(\vec c\)are unit vectors. i.e., |\(\vec a\)| = |\(\vec b\)| = |\(\vec c\)| = 1 And \(\vec a\) + \(\vec b\) + \(\vec c\) = \(\vec 0\) Then \((\vec a+\vec b+\vec c).(\vec a+\vec b+\vec c)=\vec 0.\vec...
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