Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Vector Algebra

Multiple Choice Questions

301.

The value of $straight i with hat on top. space left parenthesis straight j with hat on top space cross times space straight k with hat on top right parenthesis. space plus space straight j with hat on top. space left parenthesis straight i with hat on top space cross times space straight k with hat on top right parenthesis space plus space straight k with hat on top. space left parenthesis straight i with hat on top space cross times space straight j with hat on top right parenthesis$ is

0
-1
1
1

96 Views

302. Area of a rectangle having vertices A, B, C and D with position vectors

negative straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space straight i with hat on top space plus space 1 half straight j with hat on top space plus space 4 space straight k with hat on top comma space space space space straight i with hat on top space minus space 1 half straight j with hat on top space plus 4 straight k with hat on top space and space minus straight i with hat on top space minus space 1 half straight j with hat on top space plus space 4 straight k with hat on top comma

respectively is

$1 half$
1
2
2

74 Views

Long Answer Type

303. If A, B and C are the vertices of a triangle ABC, prove Sine Formula that

fraction numerator straight a over denominator sin space straight A end fraction space equals space fraction numerator straight b over denominator sin space straight B end fraction space equals space fraction numerator straight c over denominator sin space straight C end fraction.

79 Views

304. Using vectors, prove that sin (A + B) = sin A + cos B + cos A sin B.

75 Views

305. Prove by vector method that sin (A – B) = sin A cos B – cos A sin B

92 Views

306. Prove that the parallelograms on the same base and between the same parallels are equal in area.

91 Views

307. If D, E, F are the mid points of the sides of triangle ABC, prove that

area left parenthesis increment DEF right parenthesis space equals space 1 fourth area space left parenthesis increment thin space ABC right parenthesis.

88 Views

Short Answer Type

308.

find space straight lambda space and space straight mu space if open parentheses straight i with hat on top plus space 3 space straight j with hat on top space plus space 9 space straight k with hat on top close parentheses space space straight x space space left parenthesis 3 space straight i with hat on top plus straight lambda space straight j with hat on top plus space straight mu space straight k with hat on top right parenthesis space equals space 0

928 Views

309. $If space straight a with rightwards arrow on top equals 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top comma then space find space straight a space vector space parallel space to space the space vector space straight a with rightwards arrow on top plus straight b with rightwards arrow on top.$

Given comma straight a with rightwards arrow space on top equals space 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top therefore space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space equals space open parentheses 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top close parentheses space plus space open parentheses 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top close parentheses equals 6 space straight i with hat on top space minus space 3 straight j with hat on top space plus space 2 straight k with hat on top unit space vector space parallel space to space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis space space equals space fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top over denominator vertical line straight a with rightwards arrow on top plus straight b with rightwards arrow on top vertical line end fraction equals space fraction numerator 6 space straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top over denominator square root of 36 plus 9 plus 4 end root end fraction equals space fraction numerator 6 space straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top over denominator square root of 49 end fraction equals fraction numerator 6 space straight i with hat on top over denominator 7 end fraction minus fraction numerator 3 straight j with hat on top over denominator 7 end fraction plus fraction numerator 2 straight k with hat on top over denominator 7 end fraction

1199 Views

310.

If $straight a with rightwards arrow on top space equals space 2 straight i with hat on top plus straight j with hat on top plus 3 straight k with hat on top space space space and space straight b with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 5 straight j with hat on top space minus space 2 straight k with hat on top comma space then space find space open vertical bar straight a with rightwards arrow on top cross times space straight b with rightwards arrow on top close vertical bar.$

1702 Views