Important Questions of Vector Algebra Mathematics | Zigya

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 Multiple Choice QuestionsShort Answer Type

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141.

If straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space plus space 9 straight k with hat on top space and space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space straight lambda straight j with hat on top space plus space 3 straight k with hat on top comma find the value of straight lambda so that straight a with rightwards arrow on top plus straight b with rightwards arrow on top is perpendicular to straight a with rightwards arrow on top minus straight b with rightwards arrow on top.

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142.

Let straight a with rightwards arrow on top space equals space 5 straight i with hat on top space minus space straight j with hat on top space plus space 7 straight k with hat on top and straight b with rightwards arrow on top space equals straight i with hat on top minus straight j with hat on top plus straight lambda straight k with hat on top. Find straight lambda such that straight a with rightwards arrow on top plus straight b with rightwards arrow on top and straight a with rightwards arrow on top minus straight b with rightwards arrow on top are orthogonal .

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143.

Find straight lambda if the vectors 5 straight i with hat on top plus 2 straight j with hat on top minus straight k with hat on top and straight lambda straight i with hat on top space minus space straight j with hat on top space plus space 5 space straight k with hat on top are orthogonal.

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144.

If straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals negative straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top space space and space straight c with rightwards arrow on top space equals 3 straight i with hat on top space plus space straight j with hat on top such that straight a with rightwards arrow on top space plus space straight lambda straight b with rightwards arrow on top is perpendicular to straight c with rightwards arrow on top, then find the value of straight lambda.

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 Multiple Choice QuestionsLong Answer Type

145. Find the value of A such that the vectors 3 straight a with rightwards arrow on top plus space 4 straight b with rightwards arrow on top and 2 straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top are perpendicular to each other when 

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 Multiple Choice QuestionsShort Answer Type

146.

If open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of 3 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 2 space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3 comma find the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

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147. Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitude 1 and 2 respectively and such that straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1
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148.

If straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two vectors such that open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 4 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 space space and space straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space equals space 6 find the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

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149.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitudes 2  and 1 respectively, and such that straight a with rightwards arrow on top space. space straight b with rightwards arrow on top space equals space square root of 3.

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150.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitudes square root of 3 space and space 2 comma space respectively comma space and space that space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space square root of 6.

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